A particle (mass = m and charge = q ) is moving in a region in which there exists a uniform electric field E i ^ and a uniform magnetic field B k ^ . At t = 0 , the particle is at 0 , a and is moving with v i ^ . After some time, the particle is located at 2 a , 0 and has a velocity − 2 v j ^ , then which of the following is true?

Question

A particle (mass = m and charge = q ) is moving in a region in which there exists a uniform electric field E i ^ and a uniform magnetic field B k ^ . At t = 0 , the particle is at 0 , a and is moving with v i ^ . After some time, the particle is located at 2 a , 0 and has a velocity − 2 v j ^ , then which of the following is true?, E = 3 2 m v 2 q a, at the initial moment, the rate of work done by electric field is 3 4 m v 3 a, E = 3 8 m v 2 q a, at the initial moment, the rate of work done by electric field is 3 16 m v 3 a

MARKS App · Accepted Answer

By work energy theorem W mag + W ele = 1 2 m ( 2 v ) 2 - 1 2 m ( v ) 2 0 + qE 0 2 a = 3 2 mv 2 E 0 = 3 4 mv 2 qa Rate of work done at initial instant = power of electric force = qE 0 V = 3 4 mv 3 a

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