Question

In the given figure two concentric cylindrical region in which time varying magnetic field is present as shown. From the center to radius $R$ magnetic field is perpendicular into the plane varying as $d B / d t=2 k_{0}$ and in a region from $R$ to $2 R$ magnetic field is perpendicular out of the plane varying as $d B$ / $d t=4 k_{0}$. Find the induced emf across an arc $A B$ of radius $3 R$.

• A. $6 R^{2} k \theta$
• B. $5 R^{2} k \theta$
• C. $7 R^{2} k \theta$
• D. none of these

Answer 1

Answer: (B)

$\oint \vec{E} . d \vec{I}=10 \pi R^{2} k$
$E(6 \pi R)=10 \pi R^{2} k$
$E=\frac{10}{6} R x=\frac{5}{3} R k$
Induced emf across $A B=\frac{5}{3} R k 3 R \theta=5 R^{2} k \theta$