The `5xx10^(-4)` magnetic flux lines are passing through a coil of 100 turns. If the emf induced through the coil is 5mV, the time interval will be

Options

A. 1 s
B. 0.1 s
C. 0.01 s
D. 0.001 s

Explanation

To find the time interval during which the magnetic flux changes in the coil, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) in a coil is equal to the rate of change of magnetic flux through the coil.

### Given:
- Magnetic flux (Φ) = \(5 \times 10^{-4} \, \text{Wb}\) (Weber)
- Number of turns (N) = 100
- Induced emf (ε) = 5 mV = \(5 \times 10^{-3} \, \text{V}\)

### Step 1: Use Faraday’s Law
According to Faraday's law, the induced emf (ε) is given by the formula:
\[ \epsilon = -N \frac{\Delta \Phi}{\Delta t} \]
Where:
- \( \Delta \Phi \) = change in magnetic flux
- \( \Delta t \) = time interval

### Step 2: Rearranging the Formula
We can rearrange the formula to solve for \( \Delta t \):
\[ \Delta t = -N \frac{\Delta \Phi}{\epsilon} \]

### Step 3: Substitute the Values
Now, we substitute the known values into the equation. Since we are considering the change in flux from 0 to \(5 \times 10^{-4} \, \text{Wb}\), we have:
\[ \Delta \Phi = 5 \times 10^{-4} \, \text{Wb} \]
Substituting the values:
\[ \Delta t = -100 \frac{5 \times 10^{-4}}{5 \times 10^{-3}} \]

### Step 4: Simplifying the Expression
Now we simplify the expression:
\[ \Delta t = -100 \times \frac{5 \times 10^{-4}}{5 \times 10^{-3}} = -100 \times \frac{1}{10} = -10 \, \text{s} \]

### Step 5: Final Result
Since time cannot be negative, we take the absolute value:
\[ \Delta t = 0.1 \, \text{s} \]

### Conclusion
The time interval during which the magnetic flux changed is \(0.1 \, \text{s}\).

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