First slide

Magnetic flux and induced emf

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

Difficult

A

$6 R^{2} k θ$
B

$5 R^{2} k θ$
C

$7 R^{2} k θ$
D

none of these

Solution

$\begin{array}{l} \begin{array}{l} ∮ \vec{E} \cdot d \vec{l} = 10 π R^{2} k \\ E (6 π R) = 10 π R^{2} k \\ E = \frac{10}{6} R k = \frac{5}{3} R k \end{array} \\ Induced emf across A B = \frac{5}{3} R k (3 R θ) = 5 R^{2} k θ \end{array} \to$

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