A coil of area `0.4m^(2)` has 100 turns. A magnetic field of `0.04 Wb//m^-2` is acting normal to the coil surface. If this magnetic field is reduced to zero in 0.01 s, then the induced emf in the coil is

Options

A. 160V
B. 250 V
C. 270 V
D. 320 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) in a coil is equal to the negative rate of change of magnetic flux through the coil.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Area of the coil (A) = 0.4 m²
- Number of turns (N) = 100
- Initial magnetic field (B₁) = 0.04 Wb/m²
- Final magnetic field (B₂) = 0 Wb/m² (since it is reduced to zero)
- Time interval (Δt) = 0.01 s

2. **Calculate the Change in Magnetic Field (ΔB):**
\[ \Delta B = B_2 - B_1 = 0 - 0.04 = -0.04 \text{ Wb/m}^2 \]
We take the magnitude:
\[ |\Delta B| = 0.04 \text{ Wb/m}^2 \]

3. **Calculate the Change in Magnetic Flux (ΔΦ):**
The magnetic flux (Φ) through the coil is given by:
\[ \Phi = N \cdot A \cdot B \]
Therefore, the change in magnetic flux (ΔΦ) when the magnetic field changes from B₁ to B₂ is:
\[ \Delta \Phi = N \cdot A \cdot \Delta B \]
Substituting the values:
\[ \Delta \Phi = 100 \cdot 0.4 \cdot (-0.04) = -0.16 \text{ Wb} \]
Taking the magnitude:
\[ |\Delta \Phi| = 0.16 \text{ Wb} \]

4. **Calculate the Induced EMF (ε):**
Using Faraday's law:
\[ \epsilon = -\frac{\Delta \Phi}{\Delta t} \]
Substituting the values:
\[ \epsilon = -\frac{0.16}{0.01} = -16 \text{ V} \]
Taking the magnitude:
\[ \epsilon = 16 \text{ V} \]

5. **Final Calculation:**
Since we have 100 turns, the total induced emf is:
\[ \epsilon = N \cdot \left(-\frac{\Delta \Phi}{\Delta t}\right) = 100 \cdot 16 = 160 \text{ V} \]

### Conclusion:
The induced emf in the coil is **160 V**.

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