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 find the current in the coil, we can follow these steps:

### Step 1: Calculate the induced EMF (Electromotive Force)
The induced EMF (E) in a coil can be calculated using Faraday's law of electromagnetic induction, which states that the induced EMF is equal to the negative rate of change of magnetic flux through the coil. The formula is given by:

\[ E = -N \frac{d\Phi}{dt} \]

where:
- \(N\) = number of turns in the coil
- \(\frac{d\Phi}{dt}\) = rate of change of magnetic flux

Since the magnetic field is changing at a rate of \(10^8 \, \text{gauss/s}\), we need to convert this to tesla. The conversion factor is \(1 \, \text{gauss} = 10^{-4} \, \text{tesla}\).

Thus, the rate of change of magnetic field in tesla is:

\[ \frac{dB}{dt} = 10^8 \, \text{gauss/s} \times 10^{-4} \, \text{tesla/gauss} = 10^4 \, \text{tesla/s} \]

The area of the coil is given as \(10 \, \text{cm}^2\). We need to convert this to square meters:

\[ \text{Area} = 10 \, \text{cm}^2 = 10 \times 10^{-4} \, \text{m}^2 = 10^{-3} \, \text{m}^2 \]

Now we can calculate the magnetic flux change:

\[ \Phi = B \cdot A \]

The rate of change of magnetic flux (\(\frac{d\Phi}{dt}\)) is:

\[ \frac{d\Phi}{dt} = A \cdot \frac{dB}{dt} = (10^{-3} \, \text{m}^2) \cdot (10^4 \, \text{tesla/s}) = 10 \, \text{Wb/s} \]

Now substituting the values into the EMF formula:

\[ E = -N \frac{d\Phi}{dt} = -10 \cdot 10 = -100 \, \text{V} \]

The negative sign indicates direction, but we are interested in the magnitude:

\[ E = 100 \, \text{V} \]

### Step 2: Calculate the current using Ohm's Law
Now we can calculate the current (I) in the coil using Ohm's Law:

\[ I = \frac{E}{R} \]

where:
- \(E = 100 \, \text{V}\) (induced EMF)
- \(R = 20 \, \Omega\) (resistance of the coil)

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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