Question

An electron beam in a TV picture tube is accelerated through a potential difference of $V$ volts. It passes through a region of transverse magnetic induction field ($B$) and follows a circular orbit of radius ${}^{\prime }{r}^{\prime }$. The induced magnetic field ($B$) is:

• A. $\sqrt{\frac{2mV}{r}}$
• B. $\sqrt{\frac{2mVr}{e}}$
• C. $\frac{2mV}{\sqrt{er}}$
• D. $\sqrt{\frac{2mV}{{er}^2}}$

Answer 1

The correct option is D $\sqrt{\frac{2mV}{{er}^2}}$

The energy of orbiting electron provided by applied potential difference is in form of kinetic energy.

$⟹eV=\frac{1}{2}m{v}^2$

Also the force exerted by magnetic field causes the centripetal acceleration.

$⟹evB=\frac{m{v}^2}{r}$

$⟹B=\frac{mv}{re}$

$=\frac{m\sqrt{\frac{2eV}{m}}}{re}$

$=\sqrt{\frac{2mV}{e{r}^2}}$