First slide

Magnetic flux and induced emf

Question

Magnetic field B in a cylindrical region of radius r varies according to the law $B = B_{o} t$ as shown in the figure. A fixed conducting loop ABCDA of resistance R is lying in the region as shown. The current flowing through the loop is

Moderate

A

$\frac{π a^{2} B_{0}}{12 R}$
B

$\frac{π (r^{2} - a^{2}) B_{0}}{12 R}$
C

$\frac{π (b^{2} - a^{2}) B_{0}}{12 R}$
D

$\frac{π (b^{2} - r^{2}) B_{0}}{12 R}$

Solution

$\begin{array}{l} [Step 1] : i = \frac{e}{R} \\ [Step 2] : e = A \frac{d B}{d t} \\ [Step 3] := \frac{π}{6} [\frac{r^{2} - a^{2}}{2}] B_{0} \\ [Step 4] :∴ i = \frac{(r^{2} - a^{2}) π B_{0}}{12 R} \end{array}$

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