The magnetic field vector of an electromagnetic wave is given by B = B0 = i ^ + j ^ 2 c o s ( k z ω t ) ;  where i ^ , j ^  represents unit vector along x and y-axis respectively. At t = 0 s, two electric charges q1 of 4π coulomb and q2 and 2p coulomb located at ( 0 , 0 , π k ) a n d ( 0 , 0 , 3 π k ) ,  respectively, have the same velocity of 0.5 c   i ^ (where c is the velocity of light). The ratio of the force acting on charge q1 to q2 is:

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>1</mn> <mo>:</mo> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>
Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mo>:</mo> <mn>1</mn> </mrow> </math> </span></p>
Option 3 - <p>2 : 1</p>
Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>2</mn> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mo>:</mo> <mn>1</mn> </mrow> </math> </span></p>
9 Views|Posted 7 months ago
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V
7 months ago
Correct Option - 3
Detailed Solution:

Force on q1 :

F q 1 = q ( V * B ) = 4 π ( 0 . 5 c i ^ ) * B 0 2 ( c o s ( k z ω t ) i ^ + c o s ( k z w t ) j ^ )

= 4 π ( 0 . 5 c ) ( B 0 2 ) c o s ( k π k ) k ^      

For on q2:

= 2 π ( 0 . 5 c ) ( B 0 2 ) c o s ( k 3 π k ) k ^

So ratio will be 2 : 1

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Physics Electromagnetic Waves 2025

Physics Electromagnetic Waves 2025

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