Question

When a proton is released from rest in a room and it starts with an initial acceleration a0 towards east. When it is projected with a speed v0 it moves with an initial acceleration 3a0 towards west. The electric and magnetic fields in the room are

Answer 1

Acceleration due to the electric field,
$a_0=\frac{eE}{m}$
$\Rightarrow E=\frac{m{a}_0}{e}$ towards west.
Under the action of electric field as well as the magnetic field.
$\frac{e{v}_{0}B+eE}{m}=3a_{0}e{v}_{0}B=3m{a}_0-eE=3m{a}_0-m{a}_0=2m{a}_0$
$\Rightarrow B=\frac{2m{a}_0}{e{v}_0}$ downwards.