A coil of area 10 `cm^2` has 200 turns. Magnetic field of 0.1 `Wb//m^2` is perpendicular to the plane of the coil. The field is reduced to zero in 0.1 s, the induced emf in the coil is

Options

A. 1V
B. 0.2V
C. 2V
D. 0

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the Given Data
We have a coil with:
- Area \( A = 10 \, \text{cm}^2 = 10 \times 10^{-4} \, \text{m}^2 \)
- Number of turns \( N = 200 \)
- Initial magnetic field \( B_i = 0.1 \, \text{Wb/m}^2 \)
- Final magnetic field \( B_f = 0 \, \text{Wb/m}^2 \)
- Time duration \( \Delta t = 0.1 \, \text{s} \)

### Step 2: Calculate the Change in Magnetic Field
The change in magnetic field \( \Delta B \) is given by:
\[ \Delta B = B_f - B_i = 0 - 0.1 = -0.1 \, \text{Wb/m}^2 \]

### Step 3: Calculate the Change in Magnetic Flux
The magnetic flux \( \Phi \) through the coil is given by:
\[ \Phi = B \cdot A \]
The change in magnetic flux \( \Delta \Phi \) can be calculated as:
\[ \Delta \Phi = A \cdot \Delta B = A \cdot (B_f - B_i) = A \cdot (-0.1) \]
Substituting the values:
\[ \Delta \Phi = (10 \times 10^{-4} \, \text{m}^2) \cdot (-0.1) = -10 \times 10^{-5} = -1 \times 10^{-4} \, \text{Wb} \]

### Step 4: Calculate the Induced EMF
The induced EMF \( \mathcal{E} \) in the coil is given by Faraday's law of electromagnetic induction:
\[ \mathcal{E} = -N \frac{\Delta \Phi}{\Delta t} \]
Substituting the values:
\[ \mathcal{E} = -200 \cdot \frac{-1 \times 10^{-4}}{0.1} \]
Calculating this gives:
\[ \mathcal{E} = 200 \cdot \frac{1 \times 10^{-4}}{0.1} = 200 \cdot 10^{-3} = 0.2 \, \text{V} \]

### Final Answer
The induced EMF in the coil is \( \mathcal{E} = 0.2 \, \text{V} \).

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