A wire loop of area `0.2 m^(2)` has a resistance of `20 ohm . (A)` magnetic field, normal to the loop, initially has a magnifude of `0.25 T` and is reduced to zero at a uniform rate in `10^(-4) s`. Estimate the resulting current in ampere.

Answer

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

### Step 1: Calculate the change in magnetic flux (ΔΦ)

The magnetic flux (Φ) through the loop is given by the formula:
\[ \Phi = B \cdot A \]
where \( B \) is the magnetic field strength and \( A \) is the area of the loop.

Initially, the magnetic field \( B_i = 0.25 \, T \) and the area \( A = 0.2 \, m^2 \).

So, the initial magnetic flux \( \Phi_i \) is:
\[ \Phi_i = B_i \cdot A = 0.25 \, T \cdot 0.2 \, m^2 = 0.05 \, Wb \]

When the magnetic field is reduced to zero, the final magnetic flux \( \Phi_f \) is:
\[ \Phi_f = 0 \, Wb \]

Thus, the change in magnetic flux \( \Delta \Phi \) is:
\[ \Delta \Phi = \Phi_f - \Phi_i = 0 - 0.05 = -0.05 \, Wb \]

### Step 2: Calculate the induced EMF (ε)

According to Faraday's law, the induced electromotive force (EMF) is given by:
\[ \epsilon = -\frac{\Delta \Phi}{\Delta t} \]
where \( \Delta t \) is the time interval over which the change occurs.

Given \( \Delta t = 10^{-4} \, s \), we can calculate the induced EMF:
\[ \epsilon = -\frac{-0.05 \, Wb}{10^{-4} \, s} = \frac{0.05}{10^{-4}} = 500 \, V \]

### Step 3: Calculate the current (I) using Ohm's Law

Ohm's law states that:
\[ I = \frac{\epsilon}{R} \]
where \( R \) is the resistance of the loop.

Given \( R = 20 \, \Omega \), we can now calculate the current:
\[ I = \frac{500 \, V}{20 \, \Omega} = 25 \, A \]

### Final Answer

The resulting current in the loop is \( 25 \, A \).

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