Question

An electron having mass '$m$' and kinetic energy $E$ enter in the uniform magnetic field $B$ perpendicularly, then its frequency will be:

• A. $\frac{eE}{qVB}$
• B. $\frac{2\pi m}{eB}$
• C. $\frac{eB}{2\pi m}$
• D. $\frac{2m}{eBE}$

Answer 1

Answer: (C)

$\frac{eB}{2\pi m}$

It velocity of particle is perpendicular to the magnetic field,the particles moves in a circle.The centripetal force is experienced by electron is $qVB$

$\frac{m{v}^2}{r}=qVB\frac{mv}{r}=qB$

$mw=qB$

$w=qB/m$

$f=\frac{qB}{2\pi m}$

Frequency$=\frac{eB}{2\pi m}$