Question

Column I shows the cylindrical region of radius $r$ where a downward magnetic field $\overrightarrow{B}$ exists, where $\overrightarrow{B}$ is increasing at the rate of $dB/dt$. A rod $PQ$ is placed in different situation as shown. Match the column I with the current statement in column II regarding the induced emf in rod.

Answer 1

Note:- $e=\frac{-d\varphi }{dt}=\frac{-d}{dt}BA\cos \theta$

(A) $\Rightarrow$ Induced emf

$e_1<\frac{dB}{dt}\times \frac{r^2\theta }{2}$

Since the rod is inside and its does'not cover the entire sector.

(B) Here as Q is nearer to the field thus Q is positive w.r.t P.

(C) As the magnetic field is felt only in the area of the sector having angle ${}^{\prime }{\theta }^{\prime }$.

$\therefore$Induced emf

$e=\frac{1}{2}{r}^2\theta \frac{dB}{dt}$

(D) Similer to (B), point Q lies inside the field, thus Q is positive w.r.t P.