{"id":8166,"date":"2023-05-01T06:34:03","date_gmt":"2023-05-01T06:34:03","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=8166"},"modified":"2024-05-25T06:48:54","modified_gmt":"2024-05-25T06:48:54","slug":"electric-field-equation","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/electric-field-equation.htm","title":{"rendered":"Electric field equation","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

3 questions about Electric field equation<\/span><\/p>\n

1. A conducting ball with a radius of 10 cm has an electric charge of 500 \u03bcC. Points A, B, and C lie in line with the center of the ball at a distance of 12 cm, 10 cm and 8 cm respectively from the center of the ball. Calculate the electric field strength at points A, B, and C!<\/span><\/p>\n

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

The radius of the conducting ball (R) = 10 cm = 0.1 m<\/span><\/p>\n

Electric charge (q) = 500 \u03bcC = 500 x 10-6<\/sup> C<\/span><\/p>\n

rA<\/sub> = 12 cm = 0,12 m<\/span><\/p>\n

rB<\/sub> = 10 cm = 0,1 m<\/span><\/p>\n

rC<\/sub> = 8 cm = 0,08 m<\/span><\/p>\n

Coulomb constant (k) = 9 x 109<\/sup><\/span><\/p>\n

Wanted:<\/u> The electric field strength at point A (EA<\/sub>), at point B (EB<\/sub>) and at point C (EC<\/sub>)<\/span><\/p>\n

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

a) The electric field strength at point A<\/span><\/p>\n

EA<\/sub> = k q \/ rA<\/sub>2<\/sup> = (9 x 109<\/sup>)(500 x 10-6<\/sup>) \/ (0,12)2<\/sup> = (4500 x 103<\/sup>) \/ 0,0144 = 312500 x 103<\/sup> = 3,125 x 108 <\/sup>N\/C<\/span><\/p>\n

b) The electric field strength at point B<\/span><\/p>\n

EB<\/sub> = k q \/ rB<\/sub>2<\/sup> = (9 x 109<\/sup>)(500 x 10-6<\/sup>) \/ (0,1)2<\/sup> = (4500 x 103<\/sup>) \/ 0,01 = 450.000 x 103<\/sup> = 4,5 x 108 <\/sup>N\/C<\/span><\/p>\n

c) The electric field strength at point C<\/span><\/p>\n

EC<\/sub> = 0 for being in the ball.<\/span><\/p>\n

2. If a test charge of 4 nC is placed at a point, the charge experiences a force of 5 \u00d7 10 – 4 N. What is the magnitude of the electric field E at that point?<\/span><\/p>\n

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

Test electric charge (q) = 4 nC = 4 x 10-9<\/sup> Coulomb<\/span><\/p>\n

Electric force (F) = 5 \u00d7 10-4<\/sup> N <\/span><\/p>\n

Wanted:<\/u> The magnitude of the electric field (E)<\/span><\/p>\n

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

E = F \/ q = (5 \u00d7 10-4<\/sup>) \/ (4 x 10-9<\/sup>) = 1,25 x 105 <\/sup>N\/C<\/span><\/p>\n

3. Two charges qB<\/sub> = 12 \u03bcC and qC<\/sub> = 9 \u03bcC are placed at the vertices of a right triangle as in Fig. Determine the electric field strength felt at point A!<\/span><\/p>\n

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

Charge at point B (qB) = 12 \u03bcC = 12 x 10-6<\/sup> C<\/span><\/p>\n

Charge at point C (qC) = 9 \u03bcC = 9 x 10-6<\/sup> C<\/span><\/p>\n

Coulomb constant (k) = 9 x 109<\/sup><\/span><\/p>\n

rAC<\/sub> = 4 cm = 0,04 m<\/span><\/p>\n

rAB<\/sub> = 3 cm = 0,03 m<\/span><\/p>\n

Wanted:<\/u> electric field strength at point A\"Electric<\/span><\/p>\n

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

EAC<\/sub> = k q \/ r2<\/sup> = (9 x 109<\/sup>)(9 x 10-6<\/sup>) \/ (0,04)2<\/sup> = 81 x 103<\/sup> \/ 0,0016 = 5,0 x 107<\/sup> N\/C<\/span><\/p>\n

EAB<\/sub> = k q \/ r2<\/sup> = (9 x 109<\/sup>)(9 x 10-6<\/sup>) \/ (0,03)2<\/sup> = 81 x 103<\/sup> \/ 0,0009 = 9,0 x 107<\/sup> N\/C<\/span><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

3 questions about Electric field equation 1. A conducting ball with a radius of 10 cm has an electric charge of 500 \u03bcC. Points A, B, and C lie in line with the center of the ball at a distance of 12 cm, 10 cm and 8 cm respectively from the center of the ball. … 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":"3","_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 field equation","_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-8166","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\/8166","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=8166"}],"version-history":[{"count":7,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/8166\/revisions"}],"predecessor-version":[{"id":9842,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/8166\/revisions\/9842"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=8166"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=8166"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=8166"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}