{"id":8157,"date":"2023-05-01T02:25:21","date_gmt":"2023-05-01T02:25:21","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=8157"},"modified":"2024-05-25T06:49:51","modified_gmt":"2024-05-25T06:49:51","slug":"potential-difference-equation","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/potential-difference-equation.htm","title":{"rendered":"Potential difference equation","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

3 questions about Potential difference equation<\/span><\/p>\n

1. An electric charge is moved in a homogeneous electric field with a force of 2\u221a3 N a distance of 20 cm. If the direction of the force is at an angle of 30o<\/sup> to the displacement of the electric charge, what is the difference in the electric potential energy at the initial and final positions of the electric charge.<\/span><\/p>\n

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

Force (F) = 2\u221a3 N<\/span><\/p>\n

Distance (s) = 20 cm = 0.2 m<\/span><\/p>\n

Angle (\u03b8) = 30<\/span>o<\/sup><\/span><\/span><\/p>\n

Wanted:<\/u> Electric potential difference<\/span><\/p>\n

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

The work of transferring charge +q from a to b is equal to the electric potential energy difference at points a and b.<\/span><\/p>\n

\u0394EP = \u0394W<\/span><\/p>\n

If the direction of the force F with respect to the direction of charge transfer +q is angled \u03b8, then the work of charge transfer +q from a to b is:<\/span><\/p>\n

\u0394W = F \u0394s cos \u03b8 <\/span>= (<\/span>2<\/span>\u221a<\/span>3<\/span>)(0,2)(cos 30) = (0,4<\/span>\u221a<\/span>3<\/span>)(0,5<\/span>\u221a<\/span>3<\/span>) = (0,2)(3) = 0,6 Joule<\/span><\/span><\/p>\n

2. If the charge and capacity of the capacitor are known to be 5 \u00b5C and 20 \u00b5F, respectively, determine the potential difference of the capacitors.<\/span><\/p>\n

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

Electric charge (q) = 5 \u00b5C = 5 x 10-6<\/sup> C<\/span><\/p>\n

Capacitor capacity (C) = 20 \u00b5F = 20 x 10-6<\/sup> F <\/span><\/p>\n

Wanted:<\/u> Capacitor potential difference (V)<\/span><\/p>\n

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

The formula for capacitor potential difference, capacitor capacity and charge:<\/span><\/p>\n

V = q \/ C = (5 x 10-6<\/sup>) \/ 20 x 10-6<\/sup> = 5\/20 = 0,25 Volt <\/span><\/p>\n

3. Two point charges QA = -4 \u00b5C and QB = 8 \u00b5C are 16 cm apart. Determine the electric potential at a point halfway between the two charges.<\/span><\/p>\n

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

Electrical charge 1 (QA<\/sub>) = 4 x 10-6<\/sup> C<\/span><\/p>\n

Electrical charge 2 (QB<\/sub>) = 8 x 10-6<\/sup> C<\/span><\/p>\n

Distance (r) = 8 cm = 0,08 m<\/span><\/p>\n

Coulomb constant (k) = 9 \u00d7 109<\/sup> Nm2<\/sup>\/C2<\/sup><\/span><\/p>\n

Wanted:<\/u> The electric potential at C (VC<\/sub>)<\/span><\/p>\n

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

VA<\/sub> = k Q \/ r = (9 \u00d7 109<\/sup>)(4 x 10-6<\/sup>) \/ 0,08 = (36 \u00d7 103<\/sup>) \/ 0,08 = -450 Volt<\/span><\/p>\n

VB<\/sub> = k Q \/ r = (9 \u00d7 109<\/sup>)(8 x 10-6<\/sup>) \/ 0,08 = (72 \u00d7 103<\/sup>) \/ 0,08 = 900 Volt<\/span><\/p>\n

The electric potential at C (VC<\/sub>) = 900 \u2013 450 = 450 Volt<\/span><\/p>\n

\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

3 questions about Potential difference equation 1. An electric charge is moved in a homogeneous electric field with a force of 2\u221a3 N a distance of 20 cm. If the direction of the force is at an angle of 30o to the displacement of the electric charge, what is the difference in the electric potential … 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":"Potential difference 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-8157","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\/8157","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=8157"}],"version-history":[{"count":7,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/8157\/revisions"}],"predecessor-version":[{"id":9844,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/8157\/revisions\/9844"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=8157"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=8157"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=8157"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}