The magnetic flux threading a coil changes from `12xx10^(-3)" Wb to " 6xx10^(-3)` Wb in 0.1 s . Calculate the induced emf.

Answer

To solve the problem of calculating the induced electromotive force (emf) in the coil due to the change in magnetic flux, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial magnetic flux, \( \Phi_1 = 12 \times 10^{-3} \, \text{Wb} \)
- Final magnetic flux, \( \Phi_2 = 6 \times 10^{-3} \, \text{Wb} \)
- Time interval, \( \Delta t = 0.1 \, \text{s} \)

2. **Calculate the change in magnetic flux (\( \Delta \Phi \)):**
\[ \Delta \Phi = \Phi_2 - \Phi_1 = (6 \times 10^{-3} \, \text{Wb}) - (12 \times 10^{-3} \, \text{Wb}) = -6 \times 10^{-3} \, \text{Wb} \]

3. **Use the formula for induced emf (\( E \)):**
The formula for induced emf is given by:
\[ E = -\frac{\Delta \Phi}{\Delta t} \]

4. **Substitute the values into the formula:**
\[ E = -\frac{-6 \times 10^{-3} \, \text{Wb}}{0.1 \, \text{s}} = \frac{6 \times 10^{-3} \, \text{Wb}}{0.1 \, \text{s}} = 60 \times 10^{-3} \, \text{V} \]

5. **Convert to standard form:**
\[ E = 0.06 \, \text{V} \]

6. **Consider the magnitude of the induced emf:**
Since emf is a scalar quantity, we take the absolute value:
\[ |E| = 0.06 \, \text{V} \]

### Final Answer:
The induced emf is \( 0.06 \, \text{V} \).

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