Question

In the given figure the flux through the loop perpendicular to the plane of the coil and directed into the paper is varying according to the relation $\varphi =6t^2+7t+1$, where $\varphi$ is in milliweber and $t$ is in second. The magnitude of the emf induced in the loop at $t=2s$ and the direction of induce current through $R$ are

• A. 39 mV; right to left
• B. 39 mV; left to right
• C. 31 mV; right to left
• D. 31 mV; left to right

Answer 1

The correct option is D 31 mV; left to right

$\varphi =6t^2+7t+1\Rightarrow \frac{d\varphi }{dt}=12t+7$

At time, $t=2s$.

$\frac{d\varphi }{dt}=24+7=31volt$

Direction of current is from left to right according to Lenz'a law and the Flemmings right hand rule.