The magnetic flux threading a coil changes from `12 xx 10^(-3) Wb " to " 6 xx 10^(-3) Wb "in " 0.01` sec. Calculate the induced emf.

Answer

To solve the problem of calculating the induced emf when the magnetic flux changes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Initial magnetic flux, \( \Phi_i = 12 \times 10^{-3} \, \text{Wb} \)
- Final magnetic flux, \( \Phi_f = 6 \times 10^{-3} \, \text{Wb} \)
- Time interval, \( \Delta t = 0.01 \, \text{s} \)

2. **Calculate the Change in Magnetic Flux**:
- The change in magnetic flux, \( \Delta \Phi \), is given by:
\[ \Delta \Phi = \Phi_f - \Phi_i \]
- Substituting the values:
\[ \Delta \Phi = 6 \times 10^{-3} \, \text{Wb} - 12 \times 10^{-3} \, \text{Wb} = -6 \times 10^{-3} \, \text{Wb} \]

3. **Use Faraday's Law of Electromagnetic Induction**:
- The induced emf (\( \mathcal{E} \)) is given by:
\[ \mathcal{E} = -\frac{\Delta \Phi}{\Delta t} \]
- Substituting the values:
\[ \mathcal{E} = -\frac{-6 \times 10^{-3} \, \text{Wb}}{0.01 \, \text{s}} \]

4. **Calculate the Induced emf**:
- Performing the calculation:
\[ \mathcal{E} = \frac{6 \times 10^{-3}}{0.01} = 0.6 \, \text{V} \]

5. **Final Result**:
- The induced emf is:
\[ \mathcal{E} = 0.6 \, \text{V} \]