Question

In a very long solenoid of radius $R$, if the magnetic field changes at the rate of $dB/dt$. $AB=BC$. The induced emf for the triangular circuit $ABC$ shown in figure is :

• A. $R^2\left(\frac{dB}{dt}\right)$
• B. $4R^2\left(\frac{dB}{dt}\right)$
• C. $\frac{1}{2}{R}^2\left(\frac{dB}{dt}\right)$
• D. $2R^2\left(\frac{dB}{dt}\right)$

Answer 1

The correct option is A $R^2\left(\frac{dB}{dt}\right)$

Angle inside a semi-circle is a right angle:
Area of triangle $=A=\frac{AB.BC}{2}=R^2$
Faraday's Law:
$E=\frac{d\varphi }{dt}=A\frac{dB}{dt}=R^2\frac{dB}{dt}$