A coil having `200` turns has a surface area of `0.15m^(2)`. A magnetic field of strength `0.2T` applied perpendicular to this changes to `0.6T` in `0.4s`, then the induced emf in the coil is __________V.

Options

A. (a)45
B. (b)30
C. (c)15
D. (d)60

Answer

To find the induced electromotive force (emf) in the coil, we can use Faraday's law of electromagnetic induction, which states that the induced emf (E) in a coil is given by the formula:

\[ E = -n \frac{\Delta B}{\Delta t} A \]

Where:
- \( E \) = induced emf (in volts)
- \( n \) = number of turns in the coil
- \( \Delta B \) = change in magnetic field (in tesla)
- \( \Delta t \) = change in time (in seconds)
- \( A \) = area of the coil (in square meters)

### Step-by-step solution:

1. **Identify the given values:**
- Number of turns, \( n = 200 \)
- Surface area of the coil, \( A = 0.15 \, m^2 \)
- Initial magnetic field, \( B_i = 0.2 \, T \)
- Final magnetic field, \( B_f = 0.6 \, T \)
- Time interval, \( \Delta t = 0.4 \, s \)

2. **Calculate the change in magnetic field (\( \Delta B \)):**
\[ \Delta B = B_f - B_i = 0.6 \, T - 0.2 \, T = 0.4 \, T \]

3. **Calculate the rate of change of magnetic field (\( \frac{\Delta B}{\Delta t} \)):**
\[ \frac{\Delta B}{\Delta t} = \frac{0.4 \, T}{0.4 \, s} = 1 \, T/s \]

4. **Substitute the values into the induced emf formula:**
\[ E = n \cdot A \cdot \frac{\Delta B}{\Delta t} \]
\[ E = 200 \cdot 0.15 \cdot 1 \]

5. **Calculate the induced emf:**
\[ E = 200 \cdot 0.15 = 30 \, V \]

Thus, the induced emf in the coil is **30 V**.