Question

A uniform but time varying magnetic field $B=2t^3+24tT$ is present in a cylindrical region of radius $R=2.5cm$ as shown.
The force on an electron at $P$ at $t=2sec$. is

• A. $96\times {10}^{-21}N$
• B. $48\times {10}^{-21}N$
• C. $24\times {10}^{-21}N$
• D. Zero

Answer 1

The correct option is B $48\times {10}^{-21}N$

The induced Electric field inside a cylinder at a point $r$ from centre is,
$E=\frac{r}{2}\times \frac{dB}{dt}(r=\frac{R}{2})$
$E=\frac{R}{4}\times (6t+24)$
$E_{t=2}=\frac{2.5}{4}\times {10}^{-2}\times 48$
$E=0.3V{m}^{-1}$
Force on a charged particle in electric field is
$F=eE$
$F=1.6\times {10}^{-19}\times 0.3$
$F=48\times {10}^{-21}N$.