Magnetic field changes at the rate of `0.4 T //sec` . In a squre coil of side 4 cm . Kept prependicular to the field. If the resistance of the coil is `2xx10^(-3) Omega` , then induced current in coil is :-

Options

A. 0.16
B. 0.32
C. 3.2
D. 1.6

Answer

To solve the problem step by step, we will use the concepts of electromagnetic induction, specifically Faraday's law of induction and Ohm's law.

### Step 1: Identify the given values
- Rate of change of magnetic field, \( \frac{dB}{dt} = 0.4 \, \text{T/s} \)
- Side length of the square coil, \( l = 4 \, \text{cm} = 0.04 \, \text{m} \)
- Resistance of the coil, \( R = 2 \times 10^{-3} \, \Omega \)

### Step 2: Calculate the area of the square coil
The area \( A \) of the square coil can be calculated using the formula:
\[ A = l^2 \]
Substituting the value of \( l \):
\[ A = (0.04 \, \text{m})^2 = 0.0016 \, \text{m}^2 \]

### Step 3: Calculate the induced EMF using Faraday's law
According to Faraday's law of electromagnetic induction, the induced EMF \( \mathcal{E} \) is given by:
\[ \mathcal{E} = -\frac{d\Phi}{dt} \]
where \( \Phi \) is the magnetic flux. The magnetic flux \( \Phi \) is given by:
\[ \Phi = B \cdot A \]
Thus, the rate of change of flux is:
\[ \frac{d\Phi}{dt} = A \cdot \frac{dB}{dt} \]
Substituting the values:
\[ \frac{d\Phi}{dt} = 0.0016 \, \text{m}^2 \cdot 0.4 \, \text{T/s} = 0.00064 \, \text{Wb/s} \]
So, the induced EMF is:
\[ \mathcal{E} = -0.00064 \, \text{V} \]

### Step 4: Calculate the induced current using Ohm's law
Ohm's law states that:
\[ I = \frac{\mathcal{E}}{R} \]
Substituting the values of induced EMF and resistance:
\[ I = \frac{0.00064 \, \text{V}}{2 \times 10^{-3} \, \Omega} = 0.32 \, \text{A} \]

### Conclusion
The induced current in the coil is:
\[ I = 0.32 \, \text{A} \]