Question

In a setup for velocity selector, electrons moving with speed $v=\frac{E}{B}$ follow a straight line path. The electrons moving significantly faster than this speed, through the same velocity selector, will follow -

• A. a circular path
• B. a parabolic path
• C. a straight path
• D. cycloidal path

Answer 1

The correct option is D cycloidal path

If velocity is $v=\frac{E}{B}$, then,

$E=vB\Rightarrow qE=qvB\Rightarrow F_e=F_m$

But, if velocity is greater than $v=\frac{E}{B}i.e.v^{{}^{\prime }}>\frac{E}{B}$, then, $F_e<F_m$

Thus, the magnetic force will exceed the electric force experienced by the electron.

Therefore, electron will revolve due to magnetic force and will translate due to electric force.

Hence, trajectory will be a cycloidal path.