{"id":401,"date":"2017-11-13T13:48:03","date_gmt":"2017-11-13T08:18:03","guid":{"rendered":"http:\/\/physicscatalyst.com\/article\/?p=401"},"modified":"2023-12-24T17:21:46","modified_gmt":"2023-12-24T11:51:46","slug":"magnetic-force-and-electric-forces-between-two-moving-charges-2","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/magnetic-force-and-electric-forces-between-two-moving-charges-2\/","title":{"rendered":"Comparison of Magnetic Force and electric forces Between two Moving Charges"},"content":{"rendered":"

In this article we would be looking at Comparison of Magnetic Force and electric forces Between two Moving Charges<\/p>\n

Suppose two charges $q_{1}$\u00a0and $q_{2}$\u00a0are moving with velocities $v_{1}$\u00a0and $v_{2}$ respectively. Let r be the distance between the particles at any instant. Now two forces would be acting on each charges at this particular instant<\/p>\n

a) Electric Force:-<\/strong> which is given by<\/p>\n

$F_{e}=\\frac{1}{4\\pi \\varepsilon\u00a0{0}}\\frac{q{1}q_{2}}{r^{2}}$<\/p>\n

b) Magnetic Forces:- <\/strong>which is\u00a0due to the instantanous magnetic field setup by the moving charges and\u00a0\u00a0can be calculated as given below
\nThe instantanous magnetic field setup by $q_{1}$\u00a0at the point of space where $q_{2}$\u00a0is situated is given by<\/p>\n

$B=\\frac{\\mu {0}}{4\\pi}\\frac{q<\/em>{1}v_{1}sin\\theta}{r^{2}}$<\/p>\n

where $\\theta$ is the angle between $v_{1}$\u00a0and r . The magnetic force on the charge $q_{2}$\u00a0due to this magnetic field<\/p>\n

$F=q_{2}v_{2}B sin\\phi$<\/p>\n

where $\\phi$ is the angle between $v_{2}$\u00a0and B
\nSo magnetic force will be<\/p>\n

$F_{m}=\\frac{\\mu_{0}}{4\\pi}\\frac{q_{1}q_{2}v_{1}v_{2}sin\\theta sin\\phi}{r^2}$<\/p>\n

if $v=v_{2}=v_{1}$ and $\\theta =\\phi =90^0$\u00a0, then<\/p>\n

$F_{m}=\\frac{\\mu_{0}}{4\\pi}\\frac{q_{1}q_{2}v^2}{r^2}$<\/p>\n

So<\/p>\n

$\\frac{F_{m}}{F_{e}}=\\mu_{0}\\epsilon_{0}v^2$<\/p>\n

We know that<\/p>\n

$\\mu_{0}\\epsilon_{0}=\\frac{1}{c^2}$<\/p>\n

Where c is the velocity of the light in free space So ,<\/p>\n

$\\frac{F_{m}}{F_{e}}=\\left ( \\frac{v}{c} \\right )^2$<\/p>\n

In general v <<<<c So magnetic force are weaker then electric forces.<\/p>\n

Related articles<\/strong><\/p>\n

Electric Force Study Material<\/a><\/p>\n

Magnetic Force Study Material<\/a><\/p>\n

How to solve electric force and field problems<\/a><\/p>\n

Electrostatics class 12 and iitjee summary (pdf download)<\/a><\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Suppose two charges q1 and q2 are moving with velocities v1 and v2 $respectively. Let r be the distance between the particles at any instant. Now two forces would be acting on each charges at this particular instant
\na) Electric Force:- which is given by<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[14],"tags":[],"class_list":["post-401","post","type-post","status-publish","format-standard","hentry","category-physics"],"yoast_head":"\nComparison of Magnetic Force and electric forces Between two Moving Charges - 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