{"id":2407,"date":"2018-05-05T06:11:42","date_gmt":"2018-05-04T22:11:42","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=2407"},"modified":"2023-08-06T15:15:02","modified_gmt":"2023-08-06T15:15:02","slug":"electrostatic-force-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/electrostatic-force-problems-and-solutions.htm","title":{"rendered":"Electrostatic force – problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Electrostatic force – problems and solutions<\/p>\n

1. If the static electric force<\/a> is 144 N, what is the distance between both charges<\/a>… (1 <\/span><\/span>\u03bcC = 10<\/span><\/span>-6 <\/span><\/span><\/sup>C <\/span><\/span>and k = 9.10<\/span><\/span>9<\/span><\/span><\/sup> N.m<\/span><\/span>2<\/span><\/span><\/sup>.C<\/span><\/span>-2<\/span><\/span><\/sup>)<\/span><\/span><\/p>\n

\"Electrostatic<\/p>\n

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

Electric force<\/a> (F<\/span><\/span>12<\/span><\/sub>) = 144 N<\/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>) = 4 \u03bcC = 4 x 10<\/span><\/span>-6 <\/span><\/span><\/sup>C<\/span><\/span><\/p>\n

Constant (k) = <\/span><\/span>9 x 10<\/span><\/span>9<\/span><\/span><\/sup> N.m<\/span><\/span>2<\/span><\/span><\/sup>.C<\/span><\/span>-2<\/span><\/span><\/sup><\/p>\n

C = Coulomb, N = Newton, m = meter<\/i><\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Distance between both charges (r)<\/span><\/span><\/p>\n

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

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

\"Electrostatic<\/p>\n

F = the static electric force, k = <\/i><\/span><\/span>Coulomb’s constant, q = electric charge, r = distance between both charges<\/i><\/span><\/span><\/p>\n

\"Electrostatic<\/p>\n

Distance between both charges (r) = 5 x 10<\/span><\/span>-2<\/span><\/span><\/sup> meter = 5 x 10<\/span><\/span>-2<\/span><\/span><\/sup> x 10<\/span><\/span>2 <\/span><\/span><\/sup>cm = 5 cm. <\/span><\/span><\/p>\n

2. Two charges separated by a distance of r<\/span><\/span>. If the static electric force is 3.6 N, what is the distance between both charges <\/span><\/span>(1 <\/span><\/span>\u03bcC = 10<\/span><\/span>-6 <\/span><\/span><\/sup>C and <\/span><\/span>k = 9.10<\/span><\/span>9<\/span><\/span><\/sup> N.m<\/span><\/span>2<\/span><\/span><\/sup>.C<\/span><\/span>-2<\/span><\/span><\/sup>)<\/span><\/span><\/p>\n

\"Electrostatic<\/p>\n

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

Electric force (F<\/span><\/span>12<\/span><\/sub>) = 3.6 N<\/span><\/span><\/p>\n

Charge 1 (q<\/span><\/span>1<\/span><\/sub>) = 9 \u03bcC = 9 x 10<\/span><\/span>-6 <\/span><\/span><\/sup>C<\/span><\/span><\/p>\n

Charge 2 (q<\/span><\/span>2<\/span><\/sub>) = 4 \u03bcC = 4 x 10<\/span><\/span>-6 <\/span><\/span><\/sup>C<\/span><\/span><\/p>\n

Coulomb’s constant (k) = <\/span><\/span>9 x 10<\/span><\/span>9<\/span><\/span><\/sup> N.m<\/span><\/span>2<\/span><\/span><\/sup>.C<\/span><\/span>-2<\/span><\/span><\/sup><\/p>\n

C = Coulomb, N = Newton, m = meter<\/i><\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Distance between both charges (r)<\/span><\/span><\/p>\n

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

\"Electrostatic<\/p>\n

Distance between both charges (r) = 0.3 m = 0.3 x 100<\/span><\/span> cm = 30 cm. <\/span><\/span><\/p>\n

3. <\/span><\/span>Three point charges as shown in figure below. What is the magnitude of the static electric force at point A <\/span><\/span>(k = 9.10<\/span><\/span>9<\/span><\/span><\/sup> N.m<\/span><\/span>2<\/span><\/span><\/sup>.C<\/span><\/span>-2<\/span><\/span><\/sup>; 1 <\/span><\/span>\u03bc = 10<\/span><\/span>-6<\/span><\/span><\/sup>)<\/span><\/span><\/p>\n

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

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

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

Charge <\/span><\/span>C (q<\/span><\/span>C<\/span><\/sub>) = 4,5 \u03bcC = 4,5 x 10<\/span><\/span>-6 <\/span><\/span><\/sup>C<\/span><\/span><\/p>\n

Coulomb<\/span><\/span>‘s constant<\/span><\/span> (k) = <\/span><\/span>9 x 10<\/span><\/span>9<\/span><\/span><\/sup> N.m<\/span><\/span>2<\/span><\/span><\/sup>.C<\/span><\/span>-2<\/span><\/span><\/sup><\/p>\n

Distance between charge A and B <\/span><\/span>(r<\/span><\/span>AB<\/span><\/sub>) = 4 cm = 4 x 10<\/span><\/span>-2<\/span><\/span><\/sup> m<\/span><\/span><\/p>\n

Distance between charge A and C <\/span><\/span>(r<\/span><\/span>AC<\/span><\/sub>) = 3 cm = 3 x 10<\/span><\/span>-2<\/span><\/span><\/sup> m<\/span><\/span><\/p>\n

C = Coulomb, N = Newton, m = meter<\/i><\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The static electric force at point A<\/span><\/span><\/p>\n

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

The equation of Coulomb’s law :<\/span><\/span><\/p>\n

\"Electrostatic<\/p>\n

F = <\/i><\/span><\/span>the static electric force<\/i><\/span><\/span>, k = <\/i><\/span><\/span>Coulomb<\/i><\/span><\/span>‘s constant<\/i><\/span><\/span>, q = <\/i><\/span><\/span>electric charge<\/i><\/span><\/span>, r = <\/i><\/span><\/span>distance between both charges<\/i><\/span><\/span><\/p>\n

\"Electrostatic<\/p>\n

\"Electrostatic<\/p>\n

The static electric force at point A :<\/span><\/span><\/p>\n

\"Electrostatic<\/p>\n

4. Three-point charges as shown in the figure below. What is the magnitude of Coulomb force experienced by Charge B <\/span><\/span><\/span>(k = 9.10<\/span><\/span><\/span>9<\/span><\/span><\/sup><\/span> N.m<\/span><\/span><\/span>2<\/span><\/span><\/sup><\/span>.C<\/span><\/span><\/span>-2<\/span><\/span><\/sup><\/span>; 1 <\/span><\/span><\/span>\u03bcC = 10<\/span><\/span><\/span>-6 <\/span><\/span><\/sup><\/span>C<\/span><\/span><\/span>).<\/span><\/span><\/span><\/p>\n

\"Electrostatic<\/p>\n

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

q<\/span><\/span><\/span>A<\/span><\/span><\/sub> = 10 \u00b5C = 10 x 10<\/span><\/span><\/span>-6<\/span><\/span><\/sup><\/span> C = 10<\/span><\/span><\/span>-5<\/span><\/span><\/sup><\/span> Coulomb<\/span><\/span><\/span><\/p>\n

q<\/span><\/span><\/span>B<\/span><\/span><\/sub> = 10 \u00b5C = 10 x 10<\/span><\/span><\/span>-6<\/span><\/span><\/sup><\/span> = 10<\/span><\/span><\/span>-5<\/span><\/span><\/sup><\/span> Coulomb<\/span><\/span><\/span><\/p>\n

q<\/span><\/span><\/span>C<\/span><\/span><\/sub> = 20 \u00b5C = 20 x 10<\/span><\/span><\/span>-6<\/span><\/span><\/sup><\/span> = 2 x 10<\/span><\/span><\/span>-5<\/span><\/span><\/sup><\/span> Coulomb<\/span><\/span><\/span><\/p>\n

r<\/span><\/span><\/span>AB<\/span><\/span><\/sub> = 0.1 meter = 10<\/span><\/span><\/span>-1<\/span><\/span><\/sup><\/span> m<\/span><\/span><\/span><\/p>\n

r<\/span><\/span><\/span>BC<\/span><\/span><\/sub> = 0.1 meter = 10<\/span><\/span><\/span>-1<\/span><\/span><\/sup><\/span> m<\/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

Wanted :<\/u><\/span><\/span><\/span> Coulomb force experienced by Charge B <\/span><\/span><\/span><\/p>\n

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

There are two coulomb forces act on charge B, Coulomb force between charge A and B (F<\/span><\/span><\/span>AB<\/span><\/span><\/sub>) and Coulomb force between charge B and C (F<\/span><\/span><\/span>BC<\/span><\/span><\/sub>). Coulomb force experienced by charge B is net force of F<\/span><\/span><\/span>AB<\/span><\/span><\/sub> and F<\/span><\/span><\/span>BC<\/span><\/span><\/sub>.<\/span><\/span><\/span><\/p>\n

Coulomb force between charge A and B :<\/u><\/span><\/span><\/span><\/p>\n

\"Electrostatic<\/p>\n

Charge A signed positive and charge B signed positive so that F<\/span><\/span><\/span>AB<\/span><\/span><\/sub> points to charge C.<\/span><\/span><\/span><\/p>\n

Coulomb force between charge B and C :<\/u><\/span><\/span><\/span><\/p>\n

\"Electrostatic<\/p>\n

Charge B signed positive and charge C signed positive so that F<\/span><\/span><\/span>BC<\/span><\/span><\/sub> points to charge A.<\/span><\/span><\/span><\/p>\n

Coulomb force experienced by charge B :<\/u><\/span><\/span><\/span><\/p>\n

F<\/span><\/span><\/span>B<\/span><\/span><\/sub> = F<\/span><\/span><\/span>BC <\/span><\/span><\/sub>\u2013 F<\/span><\/span><\/span>AB<\/span><\/span><\/sub> = 180 \u2013 90 = 90 N<\/span><\/span><\/span><\/p>\n

Coulomb force experienced by charge B (F<\/span><\/span><\/span>B<\/span><\/span><\/sub>) is 90 Newton. The direction of F<\/span><\/span><\/span>B<\/span><\/span><\/sub> same as the direction of F<\/span><\/span><\/span>BC <\/span><\/span><\/sub>points to charge A.<\/span><\/span><\/span><\/p>\n

5<\/span><\/span>. Determine the magnitude and direction of Coulomb force on charge B (<\/span><\/span>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>, 1 \u03bcC = 10<\/span><\/span><\/span>\u22126<\/span><\/span><\/sup><\/span> C).<\/span><\/span><\/span><\/p>\n

\"Electrostatic<\/p>\n

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

Charge <\/span><\/span>A (q<\/span><\/span>A<\/span><\/sub>) = +Q<\/span><\/span><\/p>\n

Charge <\/span><\/span>B (q<\/span><\/span>B<\/span><\/sub>) = -2Q<\/span><\/span><\/p>\n

Charge <\/span><\/span> C (q<\/span><\/span>C<\/span><\/sub>) = -Q<\/span><\/span><\/p>\n

Distance between charge A and B <\/span><\/span>(r<\/span><\/span>AB<\/span><\/sub>) = r<\/span><\/span><\/p>\n

Distance between charge B and C <\/span><\/span>(r<\/span><\/span>BC<\/span><\/sub>) = 2r<\/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

Wanted :<\/u><\/span><\/span> Magnitude and direction of Coulomb force on charge B<\/span><\/span><\/p>\n

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

Coulomb force between charge A and B :<\/span><\/span><\/p>\n

\"Electrostatic<\/p>\n

Charge A positive and charge B negative so that the direction of<\/span><\/span><\/span> F<\/span><\/span><\/span>AB <\/span><\/span><\/sub>points to charge A.<\/span><\/span><\/span><\/p>\n

Coulomb force between charge B and charge C :<\/span><\/span><\/p>\n

\"Electrostatic<\/p>\n

Charge B is negative and charge C is negative so that the direction of F<\/span><\/span><\/span>BC <\/span><\/span><\/sub>points to charge A.<\/span><\/span><\/span><\/p>\n

Net force act on charge B :<\/span><\/span><\/span><\/p>\n

F = F<\/span><\/span><\/span>AB<\/span><\/span><\/sub> + F<\/span><\/span><\/span>BC <\/span><\/span><\/sub>= 2 k Q<\/span><\/span><\/span>2<\/span><\/span><\/sup><\/span>\/r<\/span><\/span><\/span>2<\/span><\/span><\/sup><\/span> + 0.5 k Q<\/span><\/span><\/span>2<\/span><\/span><\/sup><\/span>\/r<\/span><\/span><\/span>2<\/span><\/span><\/sup><\/span> = 2.5 k Q<\/span><\/span><\/span>2<\/span><\/span><\/sup><\/span>\/r<\/span><\/span><\/span>2<\/span><\/span><\/sup><\/span> = 2.5 k Q<\/span><\/span><\/span>2<\/span><\/span><\/sup><\/span> r<\/span><\/span><\/span>-2<\/span><\/span><\/sup><\/span><\/p>\n

Direction of force points to charge A or to leftward.<\/span><\/span><\/span><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

Electrostatic force – problems and solutions 1. If the static electric force is 144 N, what is the distance between both charges… (1 \u03bcC = 10-6 C and k = 9.109 N.m2.C-2) Known : Electric force (F12) = 144 N Charge 1 (q1) = 10 \u03bcC = 10 x 10-6 C Charge 2 (q2) = … 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":"Electrostatic force - 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-2407","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\/2407","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=2407"}],"version-history":[{"count":3,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/2407\/revisions"}],"predecessor-version":[{"id":8569,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/2407\/revisions\/8569"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=2407"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=2407"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=2407"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}