{"id":1932,"date":"2018-04-18T18:22:40","date_gmt":"2018-04-18T10:22:40","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1932"},"modified":"2023-08-09T05:12:41","modified_gmt":"2023-08-09T05:12:41","slug":"electric-force-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/electric-force-problems-and-solutions.htm","title":{"rendered":"Electric force \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">Electric force \u2013 problems and solutions<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">1<\/span><span style=\"color: #000000;\">. <\/span><span style=\"color: #000000;\">Three <a href=\"https:\/\/gurumuda.net\/physics\/types-of-electric-charges-problems-and-solutions.htm\" target=\"_blank\" rel=\"noopener\">charges<\/a> as shown in the figure below<\/span>. What is the <a href=\"https:\/\/gurumuda.net\/physics\/electric-force-problems-and-solutions.htm\" target=\"_blank\" rel=\"noopener\">electric force<\/a> experienced by charge B. <span style=\"color: #000000;\">k = 9 x 10<\/span><span style=\"color: #000000;\"><sup>9<\/sup><\/span><span style=\"color: #000000;\"> Nm<\/span><span style=\"color: #000000;\"><sup>2<\/sup><\/span><span style=\"color: #000000;\">C<\/span><span style=\"color: #000000;\"><sup>\u22122<\/sup><\/span><span style=\"color: #000000;\">, 1 \u03bcC = 10<\/span><span style=\"color: #000000;\"><sup>\u22126<\/sup><\/span><span style=\"color: #000000;\"> C.<\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\"><u>Known :<\/u><\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">q<\/span><sub><span style=\"color: #000000;\">A<\/span><\/sub><span style=\"color: #000000;\"> = 10 \u00b5C = 10 x 10<\/span><span style=\"color: #000000;\"><sup>-6<\/sup><\/span><span style=\"color: #000000;\"> C = 10<\/span><span style=\"color: #000000;\"><sup>-5<\/sup><\/span><span style=\"color: #000000;\"> Coulomb<img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-1933\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Electric-force-\u2013-problems-and-solutions-1.png\" alt=\"Electric force \u2013 problems and solutions 1\" width=\"224\" height=\"65\" \/><\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">q<\/span><sub><span style=\"color: #000000;\">B<\/span><\/sub><span style=\"color: #000000;\"> = 10 \u00b5C = 10 x 10<\/span><span style=\"color: #000000;\"><sup>-6<\/sup><\/span><span style=\"color: #000000;\"> = 10<\/span><span style=\"color: #000000;\"><sup>-5<\/sup><\/span><span style=\"color: #000000;\"> Coulomb<\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><span style=\"color: #000000;\">q<\/span><sub><span style=\"color: #000000;\">C<\/span><\/sub><span style=\"color: #000000;\"> = 20 \u00b5C = 20 x 10<\/span><span style=\"color: #000000;\"><sup>-6<\/sup><\/span><span style=\"color: #000000;\"> = 2 x 10<\/span><span style=\"color: #000000;\"><sup>-5<\/sup><\/span><span style=\"color: #000000;\"> Coulomb<\/span><!--more--><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">r<\/span><sub><span style=\"color: #000000;\">AB<\/span><\/sub><span style=\"color: #000000;\"> = 0.1 m = 10<\/span><span style=\"color: #000000;\"><sup>-1<\/sup><\/span><span style=\"color: #000000;\"> m<\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">r<\/span><sub><span style=\"color: #000000;\">BC<\/span><\/sub><span style=\"color: #000000;\"> = 0.1 m = 10<\/span><span style=\"color: #000000;\"><sup>-1<\/sup><\/span><span style=\"color: #000000;\"> m<\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">k = 9 x 10<\/span><span style=\"color: #000000;\"><sup>9<\/sup><\/span><span style=\"color: #000000;\"> Nm<\/span><span style=\"color: #000000;\"><sup>2<\/sup><\/span><span style=\"color: #000000;\">C<\/span><span style=\"color: #000000;\"><sup>\u22122<\/sup><\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\"><u>Wanted :<\/u><\/span> <span style=\"color: #000000;\">Electric force experienced by charge B<\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"color: #000000; font-size: 12pt; font-family: 'times new roman', times, serif;\"><u>Solution :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">There are two electric force act on charge B, that is the electric force between charge A and charge B <\/span><span style=\"color: #000000;\">(F<\/span><sub><span style=\"color: #000000;\">AB<\/span><\/sub><span style=\"color: #000000;\">) <\/span><span style=\"color: #000000;\">and also the electric force between charge B and C <\/span><span style=\"color: #000000;\">(F<\/span><sub><span style=\"color: #000000;\">BC<\/span><\/sub><span style=\"color: #000000;\">). <\/span><span style=\"color: #000000;\">The electric force experienced by charge B is the resultant of force <\/span><span style=\"color: #000000;\">F<\/span><sub><span style=\"color: #000000;\">AB<\/span><\/sub> <span style=\"color: #000000;\">and force <\/span><span style=\"color: #000000;\">F<\/span><sub><span style=\"color: #000000;\">BC<\/span><\/sub><span style=\"color: #000000;\">.<\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"color: #000000; font-size: 12pt; font-family: 'times new roman', times, serif;\"><u>The electric force between charge A and B :<\/u><\/span><\/p>\n<p style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1934\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Electric-force-\u2013-problems-and-solutions-2.png\" alt=\"Electric force \u2013 problems and solutions 2\" width=\"159\" height=\"112\" \/><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">Charge <\/span><span style=\"color: #000000;\">A <\/span><span style=\"color: #000000;\">is positive and charge B is positive so that the direction of <\/span><span style=\"color: #000000;\">F<\/span><sub><span style=\"color: #000000;\">AB<\/span> <\/sub><span style=\"color: #000000;\">points to charge <\/span><span style=\"color: #000000;\">C. <\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"color: #000000; font-size: 12pt; font-family: 'times new roman', times, serif;\"><u>The electric force between charge B and C :<\/u><\/span><\/p>\n<p style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1939\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Electric-force-\u2013-problems-and-solutions-3-1.png\" alt=\"Electric force \u2013 problems and solutions 3\" width=\"165\" height=\"113\" \/><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">Charge B is positive and charge C is positive so that <\/span><span style=\"color: #000000;\">F<\/span><sub><span style=\"color: #000000;\">BC<\/span><\/sub> <span style=\"color: #000000;\">points to charge <\/span><span style=\"color: #000000;\">A.<\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"color: #000000; font-size: 12pt; font-family: 'times new roman', times, serif;\"><u>The electric force experienced by charge B :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">F<\/span><sub><span style=\"color: #000000;\">B<\/span><\/sub><span style=\"color: #000000;\"> = F<\/span><sub><span style=\"color: #000000;\">BC <\/span><\/sub><span style=\"color: #000000;\">\u2013 F<\/span><sub><span style=\"color: #000000;\">AB<\/span><\/sub><span style=\"color: #000000;\"> = 180 \u2013 90 = 90 N.<\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">The magnitude of the electric force experienced by the charge B <\/span><span style=\"color: #000000;\">(F<\/span><sub><span style=\"color: #000000;\">B<\/span><\/sub><span style=\"color: #000000;\">) <\/span><span style=\"color: #000000;\">is <\/span><span style=\"color: #000000;\">90 Newton. <\/span><span style=\"color: #000000;\">The direction of <\/span><span style=\"color: #000000;\">F<\/span><sub><span style=\"color: #000000;\">B<\/span><\/sub> <span style=\"color: #000000;\">is the same as the direction of <\/span><span style=\"color: #000000;\">F<\/span><sub><span style=\"color: #000000;\">BC <\/span><\/sub><span style=\"color: #000000;\">, points to charge <\/span><span style=\"color: #000000;\">A.<\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">2. What is the magnitude and direction of the electric force at charge B. (<span style=\"color: #000000;\">k = 9 x 10<\/span><span style=\"color: #000000;\"><sup>9<\/sup><\/span><span style=\"color: #000000;\"> Nm<\/span><span style=\"color: #000000;\"><sup>2<\/sup><\/span><span style=\"color: #000000;\">C<\/span><span style=\"color: #000000;\"><sup>\u22122<\/sup><\/span><span style=\"color: #000000;\">, 1 \u03bcC = 10<\/span><span style=\"color: #000000;\"><sup>\u22126<\/sup><\/span><span style=\"color: #000000;\"> C)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1936\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Electric-force-\u2013-problems-and-solutions-4.png\" alt=\"Electric force \u2013 problems and solutions 4\" width=\"219\" height=\"49\" \/><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Known :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Charge A (q<sub>A<\/sub>) = +Q<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Charge B (q<sub>B<\/sub>) = -2Q<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Charge C (q<sub>C<\/sub>) = -Q<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The distance between charge A and B (r<sub>AB<\/sub>) = r<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The distance between charge B and C (r<sub>BC<\/sub>) = 2r<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">k = 9 x 10<\/span><span style=\"color: #000000;\"><sup>9<\/sup><\/span><span style=\"color: #000000;\"> Nm<\/span><span style=\"color: #000000;\"><sup>2<\/sup><\/span><span style=\"color: #000000;\">C<\/span><span style=\"color: #000000;\"><sup>\u22122<\/sup><\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Wanted :<\/u> The magnitude and the direction of the electric force at charge B.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Solution :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The electric force between charge A and B :<\/span><\/p>\n<p style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1937\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Electric-force-\u2013-problems-and-solutions-5.png\" alt=\"Electric force \u2013 problems and solutions 5\" width=\"277\" height=\"50\" \/><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">Charge A is positive and charge B is positive so that the direction of <\/span><span style=\"color: #000000;\">F<\/span><sub><span style=\"color: #000000;\">AB<\/span><\/sub> <span style=\"color: #000000;\">points to charge <\/span><span style=\"color: #000000;\">A.<\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The electric force between charge B and charge C :<\/span><\/p>\n<p style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-1938\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Electric-force-\u2013-problems-and-solutions-6-300x43.png\" alt=\"Electric force \u2013 problems and solutions 6\" width=\"300\" height=\"43\" srcset=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/sites\/28\/2018\/04\/Electric-force-\u2013-problems-and-solutions-6-300x43.png 300w, https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/sites\/28\/2018\/04\/Electric-force-\u2013-problems-and-solutions-6.png 339w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">Charge B <\/span><span style=\"color: #000000;\">i<\/span><span style=\"color: #000000;\">s negative and charge C is negative so that the direction of <\/span><span style=\"color: #000000;\">F<\/span><sub><span style=\"color: #000000;\">BC<\/span><\/sub> <span style=\"color: #000000;\">points to charge <\/span><span style=\"color: #000000;\">A.<\/span><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"color: #000000; font-size: 12pt; font-family: 'times new roman', times, serif;\">The net force acts on charge B :<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><span style=\"color: #000000;\">F = F<\/span><sub><span style=\"color: #000000;\">AB<\/span><\/sub><span style=\"color: #000000;\"> + F<\/span><sub><span style=\"color: #000000;\">BC <\/span><\/sub><span style=\"color: #000000;\">= 2 k Q<\/span><span style=\"color: #000000;\"><sup>2<\/sup><\/span><span style=\"color: #000000;\">\/r<\/span><span style=\"color: #000000;\"><sup>2<\/sup><\/span><span style=\"color: #000000;\"> + 0.5 k Q<\/span><span style=\"color: #000000;\"><sup>2<\/sup><\/span><span style=\"color: #000000;\">\/r<\/span><span style=\"color: #000000;\"><sup>2<\/sup><\/span><span style=\"color: #000000;\"> = 2.5 k Q<\/span><span style=\"color: #000000;\"><sup>2<\/sup><\/span><span style=\"color: #000000;\">\/r<\/span><span style=\"color: #000000;\"><sup>2<\/sup><\/span><span style=\"color: #000000;\"> = 2.5 k Q<\/span><span style=\"color: #000000;\"><sup>2<\/sup><\/span><span style=\"color: #000000;\"> r<\/span><span style=\"color: #000000;\"><sup>-2<\/sup><\/span> <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"color: #000000; font-size: 12pt; font-family: 'times new roman', times, serif;\">The direction of the electric force points to charge A (leftward).<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">3. Two electric charges, shown in the figure below. Charge at point A is 8 \u00b5C and the electric force acts on both charges is 45 N. If charge A moved rightward 1 cm, what is the attractive force acts on both charges. k = 9.10<sup>9<\/sup> Nm<sup>2<\/sup>.C<sup>-2<\/sup>.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Known :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Electric charge at point A (q<sub>A<\/sub>) = 8 \u00b5C = 8 x 10<sup>-6<\/sup> Coulomb<img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-1940\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Electric-force-\u2013-problems-and-solutions-7.png\" alt=\"Electric force \u2013 problems and solutions 7\" width=\"195\" height=\"53\" \/><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Electric force acts on both charges (F) = 45 Newton<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The distance between both charges (r<sub>AB<\/sub>) = 4 cm = 0.04 meters = 4 x 10<sup>-2<\/sup> meters <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Constant (k) = 9 x 10<sup>9<\/sup> Nm<sup>2<\/sup>.C<sup>-2<\/sup> <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Wanted :<\/u> The electric force between both charges if charge A moved to rightward 1 cm.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Solution :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Electric charge at point B <\/u>:<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><b>The equation of the electric force :<br \/>\n<\/b><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = k (q<sub>A<\/sub>)(q<sub>B<\/sub>) \/ r<sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F r<sup>2 <\/sup>= k (q<sub>A<\/sub>)(q<sub>B<\/sub>) <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>B<\/sub> = F r<sup>2 <\/sup>\/ k (q<sub>A<\/sub>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><b>Electric charge at point B<\/b> :<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>B<\/sub> = (45)(4 x 10<sup>-2<\/sup>)<sup>2 <\/sup>\/ (9 x 10<sup>9<\/sup>)(8 x 10<sup>-6<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>B<\/sub> = (45)(16 x 10<sup>-4<\/sup>) \/ 72 x 10<sup>3<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>B<\/sub> = (720 x 10<sup>-4<\/sup>) \/ (72 x 10<sup>3<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>B<\/sub> = 10 x 10<sup>-7 <\/sup>Coulomb<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>The electric force between the electric charge A and B :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">If charge at A moved rightward 1 cm then the distance between both charges is 3 cm = 0.03 meters = 3 x 10<sup>-2<\/sup> meters.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = k (q<sub>A<\/sub>)(q<sub>B<\/sub>) \/ r<sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = (9 x 10<sup>9<\/sup>)(8 x 10<sup>-6<\/sup>)(10 x 10<sup>-7<\/sup>) \/ (3 x 10<sup>-2<\/sup>)<sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = (9 x 10<sup>9<\/sup>)(80 x 10<sup>-13<\/sup>) \/ (9 x 10<sup>-4<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = (1 x 10<sup>9<\/sup>)(80 x 10<sup>-13<\/sup>) \/ (1 x 10<sup>-4<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = (80 x 10<sup>-4<\/sup>) \/ (1 x 10<sup>-4<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = 80 Newton<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">4. Two electric charges at point P and Q are separated by a distance of 10 cm, experience the attractive forces 8 Newton. If charge Q moved 5 cm to charge P, then what is the electric force. (1 \u00b5C = 10<sup>-6<\/sup> C and k = 9 x 10<sup>9<\/sup> Nm<sup>2<\/sup>.C<sup>-2<\/sup>).<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Known :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The distance between charge P and Q (r<sub>PQ<\/sub>) = 10 cm = 0.1 m = 1 x 10<sup>-1<\/sup> m <img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-1941\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Electric-force-\u2013-problems-and-solutions-8.png\" alt=\"Electric force \u2013 problems and solutions 8\" width=\"240\" height=\"78\" \/><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The electric force between charge P and Q (F) = 8 N<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Electric charge Q (q<sub>Q<\/sub>) = 40 \u00b5C = 40 x 10<sup>-6<\/sup> C<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Constant (k) = 9 x 10<sup>9<\/sup> Nm<sup>2<\/sup>.C<sup>-2<\/sup> <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Wanted :<\/u> The electric force between charge P and Q if charge Q is moved 5 cm to charge P.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Solution :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">First, calculate the electric charge P, and then calculate the electric force between both charges, if the electric charge Q is moved 5 cm to charge P.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>The electric charge <\/u><u>P<\/u> :<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>P<\/sub> = F r<sup>2 <\/sup>\/ k (q<sub>Q<\/sub>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>P<\/sub> = (8)(1 x 10<sup>-1<\/sup>)<sup>2 <\/sup>\/ (9 x 10<sup>9<\/sup>)(40 x 10<sup>-6<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>P<\/sub> = (8)(1 x 10<sup>-2<\/sup>) \/ 360 x 10<sup>3<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>P<\/sub> = (8 x 10<sup>-2<\/sup>) \/ (36 x 10<sup>4<\/sup>) <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>P<\/sub> = (1 x 10<sup>-2<\/sup>) \/ (4.5 x 10<sup>4<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>P<\/sub> = (1 \/ 4.5) x 10<sup>-6 <\/sup>Coulomb<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>The electric force between the electric charge P and Q :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">If charge at point Q is moved 5 cm to leftward then the distance between both charges is 5 cm = 0.05 meters = 5 x 10<sup>-2<\/sup> meters<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = k (q<sub>P<\/sub>)(q<sub>Q<\/sub>) \/ r<sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = (9 x 10<sup>9<\/sup>)( (1 \/ 4.5) x 10<sup>-6<\/sup>)(40 x 10<sup>-6<\/sup>) \/ (5 x 10<sup>-2<\/sup>)<sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = (2 x 10<sup>3<\/sup>)(40 x 10<sup>-6<\/sup>) \/ (25 x 10<sup>-4<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = (80 x 10<sup>-3<\/sup>) \/ (25 x 10<sup>-4<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = 3.2 x 10<sup>1<\/sup> <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = 32 Newton<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">5. The electric force experienced by charge q<sub>B<\/sub> is 8 N (1 \u00b5C = 10<sup>-6<\/sup> C and k = 9.10<sup>9<\/sup> N.m<sup>2<\/sup>.C<sup>-2<\/sup>). If charge q<sub>B <\/sub>moved 4 cm from A, then what is the electric force experienced by q<sub>B<\/sub>.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Known :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The distance between charge A and B (r<sub>AB<\/sub>) = 2 cm = 0.02 m = 2 x 10<sup>-2<\/sup> m <img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-1942\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Electric-force-\u2013-problems-and-solutions-9.png\" alt=\"Electric force \u2013 problems and solutions 9\" width=\"185\" height=\"72\" \/><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The electric force between charge A and B (F) = 8 N<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The electric charge A (q<sub>A<\/sub>) = 2 \u00b5C = 2 x 10<sup>-6<\/sup> C<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Constant (k) = 9 x 10<sup>9<\/sup> Nm<sup>2<\/sup>.C<sup>-2<\/sup> <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Wanted :<\/u> The electric force between charge A and B if the distance between both charges is 4 cm.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Solution :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">First, calculate the electric charge B, and then calculate the electric force between both charges, if the distance of both charges is 4 cm = 0.04 meters = 4 x 10<sup>-2<\/sup> meters. <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>The electric charge at <\/u><u>B<\/u> :<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>B<\/sub> = F r<sup>2 <\/sup>\/ k (q<sub>A<\/sub>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>B<\/sub> = (8)(2 x 10<sup>-2<\/sup>)<sup>2 <\/sup>\/ (9 x 10<sup>9<\/sup>)(2 x 10<sup>-6<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>B<\/sub> = (8)(4 x 10<sup>-4<\/sup>) \/ (18 x 10<sup>3<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>B<\/sub> = (32 x 10<sup>-4<\/sup>) \/ (18 x 10<sup>3<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">q<sub>B<\/sub> = (32\/18) x 10<sup>-7<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">qB = (16\/9) x 10<sup>-7 <\/sup>Coulomb<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>The electric force between charge A and B :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = k (q<sub>A<\/sub>)(q<sub>B<\/sub>) \/ r<sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = (9 x 10<sup>9<\/sup>)(2 x 10<sup>-6<\/sup>)( (16\/9) x 10<sup>-7<\/sup>) \/ (4 x 10<sup>-2<\/sup>)<sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = (18 x 10<sup>3<\/sup>)( (16\/9) x 10<sup>-7<\/sup>) \/ (16 x 10<sup>-4<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = (2 x 10<sup>3<\/sup>)(16 x 10<sup>-7<\/sup>) \/ (16 x 10<sup>-4<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = (2 x 10<sup>3<\/sup>)(1 x 10<sup>-7<\/sup>) \/ (1 x 10<sup>-4<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = (2 x 10<sup>-4<\/sup>) \/ (1 x 10<sup>-4<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F = 2 Newton <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">6. Three charges A, B and C as shown in figure below. AB = BC = 20 cm and charges is the same (q = 2\u00b5C). k = 9.10<sup>9<\/sup> N.m<sup>2<\/sup>.C<sup>-2<\/sup>, 1 \u00b5 = 10<sup>-6<\/sup>. What is the magnitude of the electric force acts on point B.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Known :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Charge at point A (q<sub>A<\/sub>) = 2 \u00b5C = 2 x 10<sup>-6<\/sup> Coulomb <img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-1943\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Electric-force-\u2013-problems-and-solutions-10.png\" alt=\"Electric force \u2013 problems and solutions 10\" width=\"153\" height=\"137\" \/><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Charge at point B (q<sub>B<\/sub>) = 2 \u00b5C = 2 x 10<sup>-6<\/sup> Coulomb <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Charge at point C (q<sub>C<\/sub>) = 2 \u00b5C = 2 x 10<sup>-6<\/sup> Coulomb<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The distance from B to C (r<sub>BC<\/sub>) = 20 cm = 0.2 meter = 2 x 10<sup>-1<\/sup> meters<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The distance from B to A (r<sub>BA<\/sub>) = 20 cm = 0.2 meter = 2 x 10<sup>-1<\/sup> meters <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">k = 9.10<sup>9<\/sup> N.m<sup>2<\/sup>.C<sup>-2<\/sup> <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Wanted :<\/u><b> <\/b>The magnitude of the electric force acts on point B<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Solution :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><b>The electric force between charges at point B and C :<\/b><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BC<\/sub> = k (q<sub>B<\/sub>)(q<sub>C<\/sub>) \/ r<sub>BC<\/sub><sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BC<\/sub> = (9 x 10<sup>9<\/sup>)(2 x 10<sup>-6<\/sup>)(2 x 10<sup>-6<\/sup>) \/ (2 x 10<sup>-1<\/sup>)<sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BC<\/sub> = (9 x 10<sup>9<\/sup>)(4 x 10<sup>-12<\/sup>) \/ (4 x 10<sup>-2<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BC<\/sub> = (36 x 10<sup>-3<\/sup>) \/ (4 x 10<sup>-2<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BC<\/sub> = 9 x 10<sup>-1<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BC<\/sub> = 0.9 Newton<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The electric charges at point B and C are positive so that the direction of the electric force F<sub>BC<\/sub> to leftward away from point C.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><b>The electric force between charges at point B and A :<\/b><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BA<\/sub> = k (q<sub>B<\/sub>)(q<sub>A<\/sub>) \/ r<sub>BA<\/sub><sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BA<\/sub> = (9 x 10<sup>9<\/sup>)(2 x 10<sup>-6<\/sup>)(2 x 10<sup>-6<\/sup>) \/ (2 x 10<sup>-1<\/sup>)<sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BA<\/sub> = (9 x 10<sup>9<\/sup>)(4 x 10<sup>-12<\/sup>) \/ (4 x 10<sup>-2<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BA<\/sub> = (36 x 10<sup>-3<\/sup>) \/ (4 x 10<sup>-2<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BA <\/sub>= 9 x 10<sup>-1<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BA<\/sub> = 0.9 Newton<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The electric charges at point B and A are positive so that the direction of the electric force F<sub>BA<\/sub> downward, away from point A.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The resultant of the electric forces :<\/span><\/p>\n<p style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1945\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Electric-force-\u2013-problems-and-solutions-11-1.png\" alt=\"Electric force \u2013 problems and solutions 11\" width=\"214\" height=\"82\" \/><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">7. Three charges Q<sub>1<\/sub>, Q<sub>2<\/sub>, and Q<sub>3<\/sub> as shown in the figure below. The length of AB = the length of BC = 30 cm. <u>Known:<\/u> k = 9.10<sup>9<\/sup> N.m<sup>2<\/sup>.C<sup>-2<\/sup> and 1 \u00b5 = 10<sup>-6<\/sup> then the resultant of the electric force at charge Q<sub>1<\/sub>.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Known :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Charge at point A (q<sub>A<\/sub>) = 3 \u00b5C = 3 x 10<sup>-6<\/sup> Coulomb\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-1946\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Electric-force-\u2013-problems-and-solutions-12.png\" alt=\"Electric force \u2013 problems and solutions 12\" width=\"189\" height=\"149\" \/><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Charge at point B (q<sub>B<\/sub>) = -10 \u00b5C = -10 x 10<sup>-6<\/sup> Coulomb <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Charge at point C (q<sub>C<\/sub>) = 4 \u00b5C = 4 x 10<sup>-6<\/sup> Coulomb<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The distance from B to C (r<sub>BC<\/sub>) = 30 cm = 0.3 meters = 3 x 10<sup>-1<\/sup> meters<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The distance from B to C (r<sub>BA<\/sub>) = 30 cm = 0.3 meters = 3 x 10<sup>-1<\/sup> meter s<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">k = 9.10<sup>9<\/sup> N.m<sup>2<\/sup>.C<sup>-2<\/sup> <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Wanted :<\/u> The resultant of the electric force at point B<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Solution :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><b>The electric force between charges at point B and C :<\/b><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BC<\/sub> = k (q<sub>B<\/sub>)(q<sub>C<\/sub>) \/ r<sub>BC<\/sub><sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BC<\/sub> = (9 x 10<sup>9<\/sup>)(10 x 10<sup>-6<\/sup>)(4 x 10<sup>-6<\/sup>) \/ (3 x 10<sup>-1<\/sup>)<sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BC<\/sub> = (9 x 10<sup>9<\/sup>)(40 x 10<sup>-12<\/sup>) \/ (9 x 10<sup>-2<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BC<\/sub> = (360 x 10<sup>-3<\/sup>) \/ (9 x 10<sup>-2<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BC<\/sub> = 40 x 10<sup>-1<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BC<\/sub> = 4 Newton<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The electric charge at point B is negative and the electric charge at point C is positive, so that the direction of the electric force F<sub>BC<\/sub> to rightward, to point C.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><b>The electric force between charges at point B and A :<\/b><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BA<\/sub> = k (q<sub>B<\/sub>)(q<sub>A<\/sub>) \/ r<sub>BA<\/sub><sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BA<\/sub> = (9 x 10<sup>9<\/sup>)(10 x 10<sup>-6<\/sup>)(3 x 10<sup>-6<\/sup>) \/ (3 x 10<sup>-1<\/sup>)<sup>2<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BA<\/sub> = (9 x 10<sup>9<\/sup>)(30 x 10<sup>-12<\/sup>) \/ (9 x 10<sup>-2<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BA<\/sub> = (270 x 10<sup>-3<\/sup>) \/ (9 x 10<sup>-2<\/sup>)<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BA<\/sub> = 30 x 10<sup>-1<\/sup><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">F<sub>BA<\/sub> = 3 Newton<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The electric charge at point B is negative and the electric charge at point A is positive, so that the direction of the electric force F<sub>BA<\/sub> upward to point A.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">The resultant of the electric force :<\/span><\/p>\n<p style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1947\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Electric-force-\u2013-problems-and-solutions-13.png\" alt=\"Electric force \u2013 problems and solutions 13\" width=\"189\" height=\"82\" \/><\/span><\/p>\n<ol>\n<li style=\"text-align: justify;\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>What is the electric force?<\/strong> <em>Answer<\/em>: Electric force is a fundamental force that occurs between objects due to their electric charges. It can be attractive (between opposite charges) or repulsive (between like charges).<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>How is the magnitude of the electric force between two point charges determined?<\/strong> <em>Answer<\/em>: The magnitude of the electric force between two point charges is given by Coulomb&#8217;s law. It&#8217;s directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">F<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">k x <\/span><span class=\"mord mathnormal mtight\">q<\/span><span class=\"msupsub\"><sub><span class=\"sizing reset-size3 size1 mtight\">1<\/span><\/sub><span class=\"vlist-s\">\u200bx <\/span><\/span><span class=\"mord mathnormal mtight\">q<\/span><span class=\"msupsub\"><sub><span class=\"sizing reset-size3 size1 mtight\">2<\/span><\/sub><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b \/ <span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">r<\/span><sup><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">2<\/span><\/span><\/span><\/sup><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, where <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">k<\/span><\/span><\/span><\/span><\/span> is Coulomb&#8217;s constant.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>What happens to the electric force if the distance between two charges is doubled?<\/strong> <em>Answer<\/em>: If the distance between two charges is doubled, the electric force becomes one-fourth of its original value, because the force varies inversely with the square of the distance.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>How does the electric force compare with the gravitational force?<\/strong> <em>Answer<\/em>: Electric forces can be both attractive and repulsive, while gravitational forces are only attractive. Additionally, for common objects and distances, electric forces are usually much stronger than gravitational forces, given that gravitational force is weaker by many orders of magnitude compared to the electric force.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>What is the principle of superposition in relation to electric forces?<\/strong> <em>Answer<\/em>: The principle of superposition states that the net electric force on a charge due to a collection of other charges is the vector sum of the forces exerted by each charge taken separately.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Why don&#8217;t we feel the electric forces in everyday objects even though they are made of charged particles?<\/strong> <em>Answer<\/em>: Everyday objects are typically electrically neutral, meaning they have equal numbers of positive and negative charges. The forces between these charges balance out, so the net electric force is zero.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>How does grounding affect the electric force on a charged object?<\/strong> <em>Answer<\/em>: Grounding a charged object allows charge to flow between the object and the Earth until the object is neutralized, effectively eliminating the net electric force on the object due to its initial charge.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Can electric force act in a vacuum?<\/strong> <em>Answer<\/em>: Yes, electric force can act in a vacuum. It doesn&#8217;t require a medium to propagate. This is evident from the way electric fields can exist and influence charged particles in space.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>What role does the electric constant (or permittivity of free space) play in determining the strength of the electric force?<\/strong> <em>Answer<\/em>: The electric constant, also known as the permittivity of free space, affects the strength of the electric force between charges. A higher permittivity would imply weaker electric forces, and vice versa. Coulomb&#8217;s constant, <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">k<\/span><\/span><\/span><\/span><\/span>, is related to this value as <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">k<\/span><span class=\"mrel\">=1\/<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<span class=\"mord mathnormal mtight\">\u03c0<\/span><span class=\"mord mathnormal mtight\">\u03b5<\/span><span class=\"msupsub\"><sub><span class=\"sizing reset-size3 size1 mtight\">0<\/span><\/sub><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/span><\/li>\n<li>\n<p style=\"text-align: justify;\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>If two charges are moving relative to each other, does the force between them change?<\/strong> <em>Answer<\/em>: If two charges are moving relative to each other, they can produce magnetic fields in addition to electric fields. This means the interaction between moving charges will not just be due to electric forces but also magnetic forces. The combined interaction is described by the electromagnetic force. So, while the electric force due to the charges doesn&#8217;t change simply because they&#8217;re moving, the overall force might change due to the magnetic effects.<\/span><\/p>\n<\/li>\n<\/ol>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>Electric force \u2013 problems and solutions 1. Three charges as shown in the figure below. What is the electric force experienced by charge B. k = 9 x 109 Nm2C\u22122, 1 \u03bcC = 10\u22126 C. Known : qA = 10 \u00b5C = 10 x 10-6 C = 10-5 Coulomb qB = 10 \u00b5C = 10 &#8230; <a title=\"Electric force \u2013 problems and solutions\" class=\"read-more\" href=\"https:\/\/gurumuda.net\/physics\/electric-force-problems-and-solutions.htm\" aria-label=\"Read more about Electric force \u2013 problems and solutions\">Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"Electric force \u2013 problems and solutions","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1932","post","type-post","status-publish","format-standard","hentry","category-solved-problems-in-basic-physics"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1932","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/comments?post=1932"}],"version-history":[{"count":2,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1932\/revisions"}],"predecessor-version":[{"id":8681,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1932\/revisions\/8681"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1932"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1932"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}