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: Understanding the Concept:
By Faraday's law, \(|\varepsilon| = \frac{d\Phi}{dt}\). The field falls at a steady rate, so the emf is the same at every instant, including \(0.25\) s.

Step 2: Area:
Radius \(= \frac{10}{\sqrt\pi}\) cm \(= \frac{0.1}{\sqrt\pi}\) m. Area \(= \pi r^2 = \pi\times\frac{0.01}{\pi} = 0.01\) m\(^2\).

Step 3: Emf:
\[ \varepsilon = A\frac{\Delta B}{\Delta t} = 0.01\times\frac{0.5}{0.5} = 0.01\ \text{V} = 10\ \text{mV} \]

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