Area of a coil is `0.16m^2`. If the magnetic field through it changes from `0.1 Wb//m^2` to `0.5 Wb//m^2` in 0.02s, then the emf induced in the coil will be-

Options

A. 1.6 V
B. 3.2 V
C. 4.8 V
D. 6.4 V

Explanation

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 (ε) is equal to the negative rate of change of magnetic flux (Φ) through the coil. The formula can be expressed as:

\[ \text{emf} = -\frac{d\Phi}{dt} \]

Where:
- \( \Phi = B \cdot A \) (magnetic flux)
- \( B \) is the magnetic field strength
- \( A \) is the area of the coil

Given:
- Area of the coil, \( A = 0.16 \, m^2 \)
- Initial magnetic field, \( B_i = 0.1 \, Wb/m^2 \)
- Final magnetic field, \( B_f = 0.5 \, Wb/m^2 \)
- Time interval, \( dt = 0.02 \, s \)

### Step 1: Calculate the change in magnetic field (db)
\[ db = B_f - B_i = 0.5 \, Wb/m^2 - 0.1 \, Wb/m^2 = 0.4 \, Wb/m^2 \]

### Step 2: Calculate the rate of change of magnetic field (db/dt)
\[ \frac{db}{dt} = \frac{0.4 \, Wb/m^2}{0.02 \, s} = 20 \, Wb/m^2/s \]

### Step 3: Calculate the induced emf (ε)
Using the formula for induced emf:
\[ \text{emf} = A \cdot \frac{db}{dt} \]
Substituting the values:
\[ \text{emf} = 0.16 \, m^2 \cdot 20 \, Wb/m^2/s = 3.2 \, V \]

### Final Answer:
The induced emf in the coil is \( 3.2 \, V \).

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