{"id":1307,"date":"2018-03-02T08:00:28","date_gmt":"2018-03-02T00:00:28","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1307"},"modified":"2018-03-02T08:00:28","modified_gmt":"2018-03-02T00:00:28","slug":"coulombs-law-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/coulombs-law-problems-and-solutions.htm","title":{"rendered":"Coulomb’s law \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. Two point charges, Q<\/span><\/span>A <\/span><\/sub>= <\/span><\/span>+8 \u03bcC and Q<\/span><\/span><\/span>B<\/span><\/span><\/sub> = -5 \u03bcC, are separated by a distance r = 10 cm. What is the magnitude of the electric force<\/a>. The constant k = 8.988 x 10<\/span><\/span><\/span>9<\/span><\/span><\/sup><\/span> Nm<\/span><\/span><\/span>2<\/span><\/span><\/sup><\/span>C<\/span><\/span><\/span>\u22122 <\/span><\/span><\/sup><\/span>= 9 x 10<\/span><\/span><\/span>9<\/span><\/span><\/sup><\/span> Nm<\/span><\/span><\/span>2<\/span><\/span><\/sup><\/span>C<\/span><\/span><\/span>\u22122<\/span><\/span><\/sup><\/span>. <\/span><\/span><\/span><\/p>\n

\"Coulomb's<\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Charge<\/a> A (q<\/span><\/span>A<\/span><\/sub>) = <\/span><\/span>+8 \u03bcC = +8 x 10<\/span><\/span><\/span>-6<\/span><\/span><\/sup><\/span> C<\/span><\/span><\/span><\/p>\n

Charge B (q<\/span><\/span><\/span>B<\/span><\/span><\/sub>) = \u00ad-5 \u03bcC = -5 x 10<\/span><\/span><\/span>-6<\/span><\/span><\/sup><\/span> C<\/span><\/span><\/span><\/p>\n

k = 9 x 10<\/span><\/span><\/span>9<\/span><\/span><\/sup><\/span> Nm<\/span><\/span><\/span>2<\/span><\/span><\/sup><\/span>C<\/span><\/span><\/span>\u22122<\/span><\/span><\/sup><\/span><\/p>\n

The distance<\/a> between charge A and B (r<\/span><\/span><\/span>AB<\/span><\/span><\/sub>) = 10 cm = 0.1 m<\/span><\/span><\/span><\/p>\n

Wanted <\/u><\/span><\/span>: <\/span><\/span>The magnitude of the electric force<\/span><\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

Formula of Coulomb’s law<\/a> :<\/span><\/span><\/p>\n

\"Coulomb's<\/p>\n

The magnitude of the electric force :<\/span><\/span><\/span><\/p>\n

\"Coulomb's<\/p>\n\n

2. Two charged particles as shown in figure below. Q<\/span><\/span>P<\/span><\/sub> = +10 \u03bcC and Q<\/span><\/span>q<\/span><\/sub> = +20 \u03bcC <\/span><\/span>are separated by a distance r = 10 cm. What is the magnitude of the electrostatic force.<\/span><\/span><\/span><\/p>\n

\"Coulomb's<\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Charge P (Q<\/span><\/span>P<\/span><\/sub>) = +10 \u03bcC = +10 x 10<\/span><\/span>-6<\/span><\/span><\/sup> C<\/span><\/span><\/p>\n

Charge Q (Q<\/span><\/span>Q<\/span><\/sub>) = +20 \u03bcC = +20 x 10<\/span><\/span>-6<\/span><\/span><\/sup> C<\/span><\/span><\/p>\n

k = 9 x 10<\/span><\/span><\/span>9<\/span><\/span><\/sup><\/span> Nm<\/span><\/span><\/span>2<\/span><\/span><\/sup><\/span>C<\/span><\/span><\/span>\u22122<\/span><\/span><\/sup><\/span><\/p>\n

The distance between charge P and Q <\/span><\/span><\/span>(r<\/span><\/span>PQ<\/span><\/sub>) = 12 cm = 0.12 m = 12 x 10<\/span><\/span>-2<\/span><\/span><\/sup> m<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> T<\/span><\/span>he magnitude of the electric force<\/span><\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

\"Coulomb's<\/p>\n\n

3. Three charged particles are arranged in a line as shown in figure below. Charge A = -5 \u03bcC, charge B = +10 \u03bcC and charge C = -12 \u03bcC. Calculate the net electrostatic force on particle B due to the other two charges. <\/span><\/span><\/p>\n

\"Coulomb's<\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Charge A (q<\/span><\/span>A<\/span><\/sub>) = -5 \u03bcC = -5 x 10<\/span><\/span>-6<\/span><\/span><\/sup> C<\/span><\/span><\/p>\n

Charge B (q<\/span><\/span>B<\/span><\/sub>) = +10 \u03bcC = +10 x 10<\/span><\/span>-6<\/span><\/span><\/sup> C<\/span><\/span><\/p>\n

Charge C (q<\/span><\/span>C<\/span><\/sub>) = -12 \u03bcC = -12 x 10<\/span><\/span>-6<\/span><\/span><\/sup> C<\/span><\/span><\/p>\n

k = 9 x 10<\/span><\/span><\/span>9<\/span><\/span><\/sup><\/span> Nm<\/span><\/span><\/span>2<\/span><\/span><\/sup><\/span>C<\/span><\/span><\/span>\u22122<\/span><\/span><\/sup><\/span><\/p>\n

The distance between particle A and B (r<\/span><\/span>AB<\/span><\/sub>) = 6 cm = 0.06 m = 6 x 10<\/span><\/span>-2<\/span><\/span><\/sup> m<\/span><\/span><\/p>\n

The distance between particle B and C (r<\/span><\/span>BC<\/span><\/sub>) = 4 cm = 0.04 m = 4 x 10<\/span><\/span>-2<\/span><\/span><\/sup> m<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The magnitude and the direction of net electrostatic force on particle B<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

The net force on particle B is the vector sum of the force F<\/span><\/span>BA<\/span><\/sub> exerted on particle B by particle A and the force F<\/span><\/span>BC <\/span><\/sub>exerted on particle B by particle C. <\/span><\/span><\/p>\n

The force F<\/b><\/span><\/span>BA<\/b><\/span><\/sub> exerted on particle B by particle A :<\/b><\/span><\/span><\/p>\n

 <\/p>\n

\"Coulomb's<\/p>\n

The direction of the electrostatic force points to particle A (point to left). <\/span><\/span><\/p>\n

The force F<\/b><\/span><\/span>BC<\/b><\/span><\/sub> exerted on particle B by particle A :<\/b><\/span><\/span><\/p>\n

 <\/p>\n

\"Coulomb's<\/p>\n

The direction of the electrostatic force points to particle C (point to right). <\/span><\/span><\/p>\n

The net electrostatic force on particle B <\/u><\/span><\/span>:<\/span><\/span><\/p>\n

F<\/span><\/span>B<\/span><\/sub> = F<\/span><\/span>AB <\/span><\/sub>– F<\/span><\/span>BC <\/span><\/sub>= 675 N \u2013 125 N = 550 Newton.<\/span><\/span><\/p>\n

The direction of the net electrostatic force on particle B points to particle C (points to the right).<\/span><\/span><\/p>\n\n

4. +Q<\/span><\/span>1<\/span><\/sub> = 10 \u03bcC, +Q<\/span><\/span>2 <\/span><\/sub>= 50 \u03bcC and Q<\/span><\/span>3<\/span><\/sub> are separated as shown in the figure below. What is the electrostatic charge on particle 3 if the net electrostatic force on particle 2 is zero.<\/span><\/span><\/p>\n

\"Coulomb's<\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Charge 1 (q<\/span><\/span>1<\/span><\/sub>) = +10 \u03bcC = +10 x 10<\/span><\/span>-6<\/span><\/span><\/sup> C<\/span><\/span><\/p>\n

Charge 2 (q<\/span><\/span>2<\/span><\/sub>) = +50 \u03bcC = +50 x 10<\/span><\/span>-6<\/span><\/span><\/sup> C<\/span><\/span><\/p>\n

The distance between charge 1 and 2 (r<\/span><\/span>12<\/span><\/sub>) = 2 cm = 0.02 m = 2 x 10<\/span><\/span>-2<\/span><\/span><\/sup> m<\/span><\/span><\/p>\n

The distance between charge 2 and charge 3 (r<\/span><\/span>23<\/span><\/sub>) = 6 cm = 0.06 m = 6 x 10<\/span><\/span>-2<\/span><\/span><\/sup> m<\/span><\/span><\/p>\n

The net electrostatic force on particle 2 (F<\/span><\/span>2<\/span><\/sub>) = 0<\/span><\/span><\/p>\n

Wanted<\/u><\/span><\/span> : charge 3 (q<\/span><\/span>3<\/span><\/sub>)<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

The net force on particle 2 is the vector<\/a> sum of the force F<\/span><\/span>21<\/span><\/sub> exerted on particle 2 by particle 1 and the force F<\/span><\/span>23<\/span><\/sub> exerted on particle 2 by particle 3. <\/span><\/span><\/p>\n

The force F<\/b><\/span><\/span>21<\/b><\/span><\/sub> exerted on particle 2 by particle 1 :<\/b><\/span><\/span><\/p>\n

\"Coulomb's<\/p>\n

The direction of the electrostatic force points to particle 3 (point to right). <\/span><\/span><\/p>\n

The force F<\/b><\/span><\/span>23<\/b><\/span><\/sub> exerted on particle 2 by particle 3 :<\/b><\/span><\/span>\u00a0\"\"<\/p>\n

The direction of the electrostatic force points to particle 1 (point to left). <\/span><\/span><\/p>\n

The net electrostatic force on particle 2 = 0 :<\/u><\/span><\/span><\/p>\n

\"Coulomb's<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

1. Two point charges, QA = +8 \u03bcC and QB = -5 \u03bcC, are separated by a distance r = 10 cm. What is the magnitude of the electric force. The constant k = 8.988 x 109 Nm2C\u22122 = 9 x 109 Nm2C\u22122. Known : Charge A (qA) = +8 \u03bcC = +8 x 10-6 … Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","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":"Coulomb's law \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-1307","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\/1307","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=1307"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1307\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1307"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1307"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1307"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}