A coil of area `10cm^2` and 10 turns is in magnetic field directed perpendicular to the plane and changing at a rate of `10^8 gauss//s`. The resistance of coil is `20Omega`. The current in the coil will be

Options

A. `0.5A`
B. `5xx10^-3A`
C. `0.05A`
D. `5A`

Explanation

To solve the problem step by step, we need to calculate the current in the coil using the given parameters. Let's break it down:

### Step 1: Identify the given values
- Area of the coil, \( A = 10 \, \text{cm}^2 = 10 \times 10^{-4} \, \text{m}^2 = 10^{-3} \, \text{m}^2 \)
- Number of turns, \( N = 10 \)
- Rate of change of magnetic field, \( \frac{dB}{dt} = 10^8 \, \text{gauss/s} = 10^8 \times 10^{-4} \, \text{T/s} = 10^4 \, \text{T/s} \)
- Resistance of the coil, \( R = 20 \, \Omega \)

### Step 2: Calculate the electromotive force (emf)
The emf (\( \mathcal{E} \)) induced in the coil can be calculated using the formula:
\[ \mathcal{E} = N \cdot A \cdot \frac{dB}{dt} \]
Substituting the values:
\[ \mathcal{E} = 10 \cdot (10 \times 10^{-4}) \cdot (10^4) \]
Calculating this:
\[ \mathcal{E} = 10 \cdot 10^{-3} \cdot 10^4 = 10 \cdot 10^{1} = 100 \, \text{V} \]

### Step 3: Calculate the current using Ohm's Law
Using Ohm's Law, the current (\( I \)) can be calculated as:
\[ I = \frac{\mathcal{E}}{R} \]
Substituting the values:
\[ I = \frac{100 \, \text{V}}{20 \, \Omega} = 5 \, \text{A} \]

### Final Answer
The current in the coil is \( 5 \, \text{A} \).

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