A coil of 100 turns is pulled from the magnetic field where its area includes `21 xx 10^(-4)` Wb to a place where its area includes `1 xx 10^(-4)` Wb. If the time for pulling is 0.05 s, find the emf induced in the coil.

Answer

To find the induced electromotive force (emf) in the coil, we will use Faraday's law of electromagnetic induction. The formula for the induced emf (ε) is given by:

\[ \epsilon = -n \frac{d\Phi}{dt} \]

Where:
- \( n \) = number of turns in the coil
- \( \Phi \) = magnetic flux
- \( d\Phi \) = change in magnetic flux
- \( dt \) = change in time

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Number of turns, \( n = 100 \)
- Initial magnetic flux, \( \Phi_1 = 21 \times 10^{-4} \, \text{Wb} \)
- Final magnetic flux, \( \Phi_2 = 1 \times 10^{-4} \, \text{Wb} \)
- Time taken, \( dt = 0.05 \, \text{s} \)

2. **Calculate the Change in Magnetic Flux (\( d\Phi \)):**
\[ d\Phi = \Phi_2 - \Phi_1 = (1 \times 10^{-4}) - (21 \times 10^{-4}) = -20 \times 10^{-4} \, \text{Wb} \]

3. **Substitute Values into the Induced EMF Formula:**
\[ \epsilon = -n \frac{d\Phi}{dt} = -100 \left( \frac{-20 \times 10^{-4}}{0.05} \right) \]

4. **Calculate the Induced EMF:**
\[ \epsilon = 100 \left( \frac{20 \times 10^{-4}}{0.05} \right) \]
\[ = 100 \left( 400 \times 10^{-4} \right) = 40 \times 10^{-2} = 4 \, \text{V} \]

5. **Final Result:**
The induced emf in the coil is \( \epsilon = 4 \, \text{V} \).