Two coils A and B are separated by a certain distance. If a current of 4 A flows through A, a magnetic flux of `10^(-3)Wb` passes through B (no current through B). If no current passes through A and a current of 2 A passes through B, then the flux through A is.

Options

A. `5xx10^(-3)Wb`
B. `4xx10^(-4)Wb`
C. `5xx10^(-4)Wb`
D. `2xx10^(-3)Wb`

Explanation

To solve the problem, we will use the concept of mutual inductance between two coils. Here’s the step-by-step solution:

### Step 1: Understand the given information
- Coil A carries a current of 4 A, which produces a magnetic flux of \(10^{-3} \, \text{Wb}\) through coil B.
- When no current flows through coil A and a current of 2 A flows through coil B, we need to find the magnetic flux through coil A.

### Step 2: Calculate the mutual inductance (M)
The magnetic flux (\(\Phi_B\)) through coil B due to coil A can be expressed as:
\[ \Phi_B = M \cdot I_A \]
Where:
- \(\Phi_B = 10^{-3} \, \text{Wb}\)
- \(I_A = 4 \, \text{A}\)

Now, we can rearrange this equation to find the mutual inductance \(M\):
\[ M = \frac{\Phi_B}{I_A} = \frac{10^{-3}}{4} = 2.5 \times 10^{-4} \, \text{H} \]

### Step 3: Calculate the magnetic flux through coil A when current flows through coil B
Now, we need to find the magnetic flux (\(\Phi_A\)) through coil A when a current of 2 A flows through coil B. The magnetic flux through coil A due to coil B can be expressed as:
\[ \Phi_A = M \cdot I_B \]
Where:
- \(I_B = 2 \, \text{A}\)

Substituting the value of \(M\) we calculated:
\[ \Phi_A = (2.5 \times 10^{-4}) \cdot 2 = 5 \times 10^{-4} \, \text{Wb} \]

### Final Answer
The magnetic flux through coil A when 2 A flows through coil B is:
\[ \Phi_A = 5 \times 10^{-4} \, \text{Wb} \]