What is the change in magnetic flux produced in a coil in 25 s, if the induced e.m.f. In the coil is `2 mV`?

Options

A. `5 xx 10^(-2) Wb`
B. `12 xx 10^(-2) Wb`
C. `7.5 xx 10^(-2) Wb`
D. `15 xx 10^(-2) Wb`

Explanation

To solve the problem, we need to find the change in magnetic flux (ΔΦ) in a coil given the induced electromotive force (e.m.f.) and the time duration. We can use Faraday's law of electromagnetic induction, which states that the induced e.m.f. (ε) in a coil is equal to the rate of change of magnetic flux through the coil.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Induced e.m.f. (ε) = 2 mV = \(2 \times 10^{-3}\) V
- Time (t) = 25 s

2. **Use Faraday's Law:**
According to Faraday's law, the induced e.m.f. is given by the formula:
\[ \epsilon = -\frac{d\Phi}{dt} \]
where \(d\Phi\) is the change in magnetic flux and \(dt\) is the change in time.

3. **Rearranging the Formula:**
We can rearrange the formula to find the change in magnetic flux:
\[ d\Phi = -\epsilon \cdot dt \]

4. **Substituting the Values:**
Substitute the values of ε and t into the equation:
\[ d\Phi = - (2 \times 10^{-3} \, \text{V}) \cdot (25 \, \text{s}) \]

5. **Calculating the Change in Magnetic Flux:**
\[ d\Phi = - (2 \times 25) \times 10^{-3} = -50 \times 10^{-3} \, \text{Wb} \]
\[ d\Phi = -0.05 \, \text{Wb} \]
Since we are interested in the magnitude of the change in magnetic flux, we can ignore the negative sign:
\[ d\Phi = 0.05 \, \text{Wb} = 5 \times 10^{-2} \, \text{Wb} \]

### Final Answer:
The change in magnetic flux produced in the coil in 25 seconds is \(5 \times 10^{-2} \, \text{Wb}\).

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