Question

A magnetic field $4 \times 10^{-2}$ T acts at right angles to a coil of area $100$ cm$^2$ with 50 turns. The average e.m.f. induced in the coil is 0.1 V, when it is removed from the field in time 't'. The value of 't' is ______.

• A. 0.02 second
• B. 0.05 second
• C. 0.2 second
• D. 2 second

Hint:

Always immediately convert $\text{cm}^2$ to $\text{m}^2$ by multiplying by $10^{-4}$. Missing this area conversion is the most common reason for getting an answer off by multiple orders of magnitude!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
According to Faraday's Law, the induced e.m.f. is equal to the rate of change of magnetic flux linkage.

Step 2: Formula Application:
$e = N \frac{\Delta \phi}{\Delta t} = N \frac{BA}{t}$.
Note: Area $100$ cm² must be converted to m² ($100 \times 10^{-4} = 10^{-2}$ m²).

Step 3: Explanation:
$0.1 = 50 \times \frac{(4 \times 10^{-2}) \times (10^{-2})}{t}$
$0.1 = \frac{50 \times 4 \times 10^{-4}}{t}$
$0.1 = \frac{200 \times 10^{-4}}{t} = \frac{0.02}{t}$
$t = \frac{0.02}{0.1} = 0.2$ s.

Step 4: Final Answer:
The value of 't' is 0.2 second.