In a coil of area `10cm^(2)` and 10 turns, magnetic field is directed perpendicular to the plane and is changing at a rate of `10^(4)Ts^(-1)`. The resistance of the coil is `20Omega`. The current in the coil will be

Options

A. 0.5 A
B. 0.20833333333333
C. 5 A
D. `5xx10^(8)A`

Answer

To solve the problem step by step, we will follow the principles of electromagnetism, specifically Faraday's law of electromagnetic induction.

### Step 1: Understand the Given Information
- 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, \( \frac{dB}{dt} = 10^4 \, \text{T/s} \)
- Resistance of the coil, \( R = 20 \, \Omega \)

### Step 2: Calculate the Induced EMF
According to Faraday's law, the induced electromotive force (EMF) in the coil is given by:
\[ \text{EMF} = -N \frac{d\Phi}{dt} \]
Where magnetic flux \( \Phi \) is given by:
\[ \Phi = B \cdot A \]
Thus, the rate of change of magnetic flux is:
\[ \frac{d\Phi}{dt} = A \frac{dB}{dt} \]
Substituting this into the EMF equation:
\[ \text{EMF} = -N A \frac{dB}{dt} \]

### Step 3: Substitute the Values
Now we substitute the values into the equation:
\[ \text{EMF} = -10 \cdot (10 \times 10^{-4}) \cdot (10^4) \]
Calculating this step by step:
\[ \text{EMF} = -10 \cdot 10^{-3} \cdot 10^4 \]
\[ \text{EMF} = -10 \cdot 10^{1} = -100 \, \text{V} \]
The negative sign indicates the direction of the induced EMF, but we are interested in the magnitude:
\[ \text{EMF} = 100 \, \text{V} \]

### Step 4: Calculate the Current Using Ohm's Law
Ohm's law states that:
\[ I = \frac{\text{EMF}}{R} \]
Substituting the values we have:
\[ I = \frac{100 \, \text{V}}{20 \, \Omega} \]
Calculating the current:
\[ I = 5 \, \text{A} \]

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

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