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 k0 and in a region from R to 2 R magnetic field is perpendicular out of the plane varying as d B / d t=4 k0. Find the induced emf across an arc A B of radius 3 R.

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 k0 and in a region from R to 2 R magnetic field is perpendicular out of the plane varying as d B / d t=4 k0. Find the induced emf across an arc A B of radius 3 R. (A) 6 R2 k θ (B) 5 R2 k θ (C) 7 R2 k θ (D) none of these

Tardigrade Admin · Accepted Answer

oint vecE . d vecI=10 π R2 k E(6 π R)=10 π R2 k E=(10/6) R x=(5/3) R k Induced emf across A B=(5/3) R k 3 R θ=5 R2 k θ

$6 R^{2} k θ$

$5 R^{2} k θ$

$7 R^{2} k θ$

none of these

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

6R2kθ

5R2kθ

7R2kθ

none of these

∮E.dI=10πR2k E(6πR)=10πR2k E=610​Rx=35​Rk Induced emf across AB=35​Rk3Rθ=5R2kθ

$6 R^{2} k θ$

$5 R^{2} k θ$

$7 R^{2} k θ$

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