Question

A closed loop of cross-sectional area ${10}^{-2}{m}^2$ which has inductance $L=10mH$ and negligible resistance is placed in a time-varying magnetic field. Figure shows the variation of B with time for the interval of 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 :

• A. 0.1 mA
• B. 10 mA
• C. 100 mA
• D. Data insufficient

Answer 1

The correct option is C 100 mA

Induced e.m.f. $|e|=L\frac{dI}{dt}=A\frac{dB}{dt}$
$\Rightarrow {\int }_0^{I}dI={\int }_0^B\frac{A}{L}dB\Rightarrow I=\frac{A}{L}B$
$\Rightarrow I_{max}=\frac{A}{L}{B}_{max}=\frac{{10}^{-2}}{10\times {10}^{-3}}\times 0.1=0.1A=100mA$