A coil having 1000 turns forming square loop of side 10 cm is placed normal to magnetic field which increases at a rate of `1 T s^(-1)` . The induced emf is:

Options

A. `5 V`
B. `10 V`
C. `2 V`
D. `20 V`

Explanation

To find the induced EMF in the coil, we can follow these steps:

### Step 1: Identify the given values
- Number of turns (N) = 1000
- Side of the square loop (s) = 10 cm = 0.1 m (conversion to meters)
- Rate of change of magnetic field (dB/dt) = 1 T/s

### Step 2: Calculate the area of one turn of the coil
The area (A) of a square loop can be calculated using the formula:
\[ A = s^2 \]
Substituting the value of s:
\[ A = (0.1 \, \text{m})^2 = 0.01 \, \text{m}^2 \]

### Step 3: Calculate the total area of the coil
Since the coil has 1000 turns, the total area (A_total) is:
\[ A_{\text{total}} = N \times A = 1000 \times 0.01 \, \text{m}^2 = 10 \, \text{m}^2 \]

### Step 4: Use Faraday's law of electromagnetic induction to find the induced EMF
According to Faraday's law, the induced EMF (ε) can be calculated using the formula:
\[ \epsilon = -\frac{d\Phi}{dt} \]
Where Φ (magnetic flux) is given by:
\[ \Phi = B \times A \]
Since the area is constant and only the magnetic field is changing, we can express the induced EMF as:
\[ \epsilon = -A \frac{dB}{dt} \]
Substituting the values:
\[ \epsilon = -10 \, \text{m}^2 \times 1 \, \text{T/s} = -10 \, \text{V} \]
(The negative sign indicates the direction of the induced EMF according to Lenz's law, but we are interested in the magnitude.)

### Step 5: Conclusion
The induced EMF is:
\[ \epsilon = 10 \, \text{V} \]

### Final Answer:
The induced EMF is **10 V**.

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