Question

A coil of area \(3 \text{ m}^{2}\) is at right angles to a magnetic field of \(0.05 \text{ Wb/m}^{2}\). If the field is decreased to \(20%\) of its value in \(10 \text{ s}\) , the induced e.m.f. is.

• A. \(10 \text{ mV}\)
• B. \(12 \text{ mV}\)
• C. \(15 \text{ mV}\)
• D. \(20 \text{ mV}\)

Hint:

E.m.f is the rate of change of flux; flux is $B \times A$ when perpendicular.

Answer 1

The Correct Option is B

Step 1: Formula
\(e = -N \frac{\Delta \Phi}{\Delta t} = -A \frac{\Delta B}{\Delta t}\).

Step 2: Values
\(B_1 = 0.05 \text{ T}\).
\(B_2 = 20%\) of \(0.05 = 0.01 \text{ T}\).
\(\Delta B = 0.01 - 0.05 = -0.04 \text{ T}\).

Step 3: Calculation
\(e = 3 \times \frac{0.04}{10} = 3 \times 0.004 = 0.012 \text{ V}\).
\(e = 12 \text{ mV}\).
Final Answer: (B)