Question

What are the magnitude and direction of the electric field at $P_1$ when $t=3.00s$ and $r_1=0.02m$.

• A. $0.3V/m$
• B. $0.6V/m$
• C. $0.9V/m$
• D. $0.12V/m$

Answer 1

The correct option is A $0.3V/m$

At $P_1$:

$El=\frac{d\varphi }{dt}$

$E\left(2\pi r_1\right)=S\frac{dB}{dt}=\left(\pi r_1^2\right)\left(\frac{dB}{dt}\right)$

$\therefore E=\frac{r_1}{2}\left(\frac{dB}{dt}\right)=\frac{r_1}{2}[6t^2-8t]=\frac{0.2}{2}[6{\left(3\right)}^2-8(3\left)\right]$$=0.3V/m$

Direction of electric field is in the direction of induced current (anticlockwise) in an imaginary circular conducting loop passing through $P_1$.