Question

The magnetic field within a long, straight solenoid with a circular cross-section of radius $r$ is (as shown) increasing at a rate of $\alpha$ .



The rate of change of flux through a circle with radius $a$ inside the solenoid, normal to the axis of the solenoid and with centre on the solenoid axis is

• A. $\sqrt{2}\pi a^2\alpha$
• B. $\frac{1}{2}\pi a^2\alpha$
• C. $\pi a^2\alpha$
• D. $\frac{3}{2}\pi a\alpha$

Answer 1

Answer: (C)

Rate of change of flux through circle with radius $a$
$\frac{d{\varphi }_m}{dt}=A\frac{dB}{dt}=\pi a^2\alpha$