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

Options

A. `E = (3)/( 2) (( mv^(2))/(qa))`
B. at the initial moment, the rate of work done by electric field is ` ( 3)/( 4) ((m v^(3))/( a))`
C. `E = ( 3)/( 8) ((mv^(2))/( qa))`
D. at the initial moment, the rate of work done by electric field is `( 3)/( 16) ((mv^(3))/( a ))`

Answer

B