In a certain region of space, there exists a uniform and constant electric field of strength E along x-axis and uniform constant magnetic field of induction B along z-axis. A charge particle having charge q and mass m is projected with speed v parallel to x-axis from a point (a, b, 0). When the particle reaches a point 2a, `b//2`, 0 its speed becomes 2v. Find the value of electric field strength in term of m, v and co-ordinates.

Options

A. `(3)/(2)(mv^(2))/(qa)`
B. `(mv^(2))/(qB)`
C. `(2mv^(2))/(qBa)`
D. `(3)/(2)vB`

Answer

A

Explanation

Change in kinetic energy is only due to work done by electric field. Hence work done by electric field is change in` KE`:
`qEa=(1)/(2)m[(2v)^(2)-v^(2)]impliesE=(3mv^(2))/(2qa)`