Question

A conducting loop of radius \(10/[π]^{1/2}\) cm is placed perpendicular to a uniform magnetic field \(0.5\) T. The magnetic field is decreased to zero in \(0.5\) s at a steady rate. The induced emf in the circular loop at \(0.25\) s is

• A. \(1\text{ mV}\)
• B. \(10\text{ mV}\)
• C. \(100\text{ mV}\)
• D. \(5\text{ mV}\)

Hint:

The emf is \(A\,\frac{\Delta B}{\Delta t}\) and is constant for a steady rate.

Answer 1

The Correct Option is B

Step 1: Plan:
Find the change in flux over the whole interval and divide by time.

Step 2: Steps:
Initial flux $= BA = 0.5\times0.01 = 5\times10^{-3}$ Wb, final flux $= 0$. Change $= 5\times10^{-3}$ Wb in $0.5$ s.
$\varepsilon = \frac{5\times10^{-3}}{0.5} = 10^{-2}$ V $= 10$ mV. The emf is steady, so the instant $0.25$ s gives the same value.

Final Answer:
The induced emf is $10$ mV, option (B). \[ \boxed{10\ \text{mV}} \]