First slide

Faraday's law of Electromagnetic induction

Question

An equilateral triangular loop having a resistance R and length of each side l is placed in a magnetic field which is varying at $\frac{d B}{d t} = 4 T / s .$ The induced current in the loop will be

Moderate

A

$\frac{\sqrt{3}}{2} \frac{l^{2}}{R}$
B

$\frac{4}{\sqrt{3}} \frac{l^{2}}{R}$
C

$\sqrt{3} \frac{l^{2}}{R}$
D

$\frac{4}{\sqrt{3}} \frac{R}{l^{2}}$

Solution

$\begin{array}{l} ϕ = \frac{\sqrt{3}}{4} l^{2} B \\ ε = |\frac{d ϕ}{d t}| = \frac{\sqrt{3}}{4} l^{2} \frac{d B}{d t} \\ i = \frac{ε}{R} = \sqrt{3} \frac{l^{2}}{R} \end{array}$

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