First slide

Inductance

Question

A closed loop of cross-sectional area 10^-2 m² which has inductance L = 10 mH and negligible resistance is placed in a time-varying magnetic field. Figure shows
the variation of B with time for the interval 4 s. The field is perpendicular to the plane of the loop (given at t = 0, B = 0,I = 0). The value of the maximum current induced in the loop is

Moderate

A

0.1 mA
B

10 mA
C

100 mA
D

Data insufficient

Solution

$\begin{array}{l} Induced e.m.f. e = L \frac{d I}{d t} = A \frac{d B}{d t} \\ \Rightarrow \int_{0}^{I} d I = \int_{0}^{B} \frac{A}{L} d B \Rightarrow I = \frac{A}{L} B \\ \Rightarrow I_{max} = \frac{A}{L} B_{max} = \frac{10^{- 2}}{10 \times 10^{- 3}} \times 0.1 = 0.1 A = 100 mA \end{array}$

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