A particle of mass `m` having negative charge `-q` is projected at an angle `theta` with `x`-axis. There exists uniform electric field `E` and a unifrom magnetic field `B` along `x`-axis. The particle will return to its intial point once if (`n` is some integer)

Options

A. `n=(Bvcostheta)/(piE)`
B. `n=(2Bvcostheta)/(piE)`
C. `n=(Bvsintheta)/(piE)`
D. `n=(2Bvsintheta)/(piE)`

Answer

A

Explanation

Let particle completes `n` revolutions in time `t`,
then `t=nT`
`implies t=(n2pim)/(qB)`
If particle has to return to its initial point, the displacement along `x`-axis during this time should be zero.
`s_(x)=u_(x)t+(1)/(2)a_(x)t^(2)`
` implies 0=vcosthetat-(1)/(2)(qE)/(m)t^(2)`
` impliesvcostheta=(qE)/(2m)t`
` impliesvcostheta=(qE)/(2m)(n2pim)/(qB)impliesn=(Bvcostheta)/(piE)`