Question

A magnetic field $B=2t+4t^2$ (where $t=$ time) is applied perpendicular to the plane of a circular wire of radius $r$ and resistance $R$. If all the units are in $SI$, the electric charge that flows through the circular wire during $t=0s$ to $t=2s$ is:

• A. $\frac{6\pi r^2}{R}$
• B. $\frac{20\pi r^2}{R}$
• C. $\frac{32\pi r^2}{R}$
• D. $\frac{48\pi r^2}{R}$

Answer 1

The correct option is B $\frac{20\pi r^2}{R}$

Given $B=2t+4t^2$
at $t=0,B_1=0$
and at $t=2,B_2=2\times 2+4{\left(2\right)}^2$
$=4+16=20Wb/m^2$
We have $\Delta Q=\frac{\Delta \varphi }{R}=\frac{\pi r^2(B_2-B_1)}{R}$
$=\frac{\pi r^2(20-0)}{R}=\frac{20\pi r^2}{R}$