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. `5 A`
B. `0.5A`
C. `0.05A`
D. `5xx10^(8)A`

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Convert Area from cm² to m²
The area of the coil is given as \(10 \, \text{cm}^2\). We need to convert this into square meters (m²).

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

### Step 2: Convert Rate of Change of Magnetic Field from Gauss to Tesla
The rate of change of the magnetic field is given as \(10^8 \, \text{Gauss/s}\). We need to convert this into Tesla (T).

\[ 1 \, \text{Gauss} = 10^{-4} \, \text{Tesla} \]
\[ \frac{dB}{dt} = 10^8 \, \text{Gauss/s} = 10^8 \times 10^{-4} \, \text{T/s} = 10^4 \, \text{T/s} \]

### Step 3: Calculate the Induced EMF (E)
The induced electromotive force (EMF) in the coil can be calculated using the formula:

\[ E = n \frac{d\Phi}{dt} \]

Where:
- \(n\) = number of turns = 10
- \(\Phi = B \cdot A\) (magnetic flux), and \(\frac{d\Phi}{dt} = A \frac{dB}{dt}\)

Thus, we can express the induced EMF as:

\[ E = n \cdot A \cdot \frac{dB}{dt} \]

Substituting the values:

\[ E = 10 \cdot (10^{-3} \, \text{m}^2) \cdot (10^4 \, \text{T/s}) \]

### Step 4: Calculate the Induced EMF
Now, we can calculate:

\[ E = 10 \cdot 10^{-3} \cdot 10^4 = 10 \cdot 10^{1} = 100 \, \text{V} \]

### Step 5: Calculate the Current (I)
Using Ohm's law, the current can be calculated as:

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

Where \(R\) is the resistance of the coil, given as \(20 \, \Omega\).

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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