Question

A uniform magnetic field of induction $B$ is confined to a cylindrical region of radius $R$. The magnetic field is increasing at a constant rate of $dB/dtT$ $s^{-1}$. An electron placed at the point $P$ on the periphery of the field, experiences an acceleration :

• A. $\frac{1}{2}\frac{eR}{m}\frac{dB}{dt}$ toward left
• B. $\frac{1}{2}\frac{eR}{m}\frac{dB}{dt}$ toward right
• C. $\frac{eR}{m}\frac{dB}{dt}$ toward left
• D. zero

Answer 1

The correct option is A $\frac{1}{2}\frac{eR}{m}\frac{dB}{dt}$ toward left

At $P$ induced electric field, $\int E\cdot dl=-\frac{d\left(AB\right)}{dt}\Rightarrow E\left(2\pi R\right)=-\left(\pi R^2\right)\frac{dB}{dt}$

When your right thumb points in the direction opposite to the change in B your curl fingers in the direction of the induced electric field.

$E=\frac{R}{2}\frac{dB}{dt}...\left(towardright\right)$

Acceleration, $a=\frac{F}{m}=\frac{-eE}{m}=-\frac{eR}{2m}\frac{dB}{dt}...\left(towardleft\right)$