Two coils 'P' and 'Q' are separated by some distance. When a current of 3A flows through coil 'P' a magnetic flux of `10^(-3) Wb` passess through 'Q'. No current is passed through 'P' and a current of 2A passes through 'Q', the flux through of 'P' is :

Options

A. `6.67xx10^(-4) Wb`
B. `3.67xx10^(-3) Wb`
C. `6.67xx10^(-3) Wb`
D. `3.67xx10^(-4) Wb`

Answer

To solve the problem, we will use the concept of mutual inductance. Let's break down the solution step by step.

### Step 1: Understand the given information
We have two coils, P and Q, separated by some distance. When a current of 3 A flows through coil P, a magnetic flux of \(10^{-3} \, \text{Wb}\) passes through coil Q.

### Step 2: Use the formula for mutual inductance
The relationship between the magnetic flux (\(\Phi\)) through coil Q and the current (\(I_P\)) in coil P is given by the formula:
\[ \Phi_Q = M \cdot I_P \]
where \(M\) is the mutual inductance.

### Step 3: Calculate the mutual inductance
From the information provided:
\[ \Phi_Q = 10^{-3} \, \text{Wb}, \quad I_P = 3 \, \text{A} \]
Substituting these values into the formula:
\[ 10^{-3} = M \cdot 3 \]
Solving for \(M\):
\[ M = \frac{10^{-3}}{3} = \frac{1}{3} \times 10^{-3} \, \text{Wb/A} \]

### Step 4: Analyze the second scenario
Now, we need to find the flux through coil P when no current is passed through it, and a current of 2 A flows through coil Q. In this case, the roles of the coils are reversed.

### Step 5: Use the mutual inductance to find the flux through coil P
Using the same formula for mutual inductance, we can express the flux through coil P (\(\Phi_P\)) when a current \(I_Q = 2 \, \text{A}\) flows through coil Q:
\[ \Phi_P = M \cdot I_Q \]
Substituting the value of \(M\) we found earlier:
\[ \Phi_P = \left(\frac{1}{3} \times 10^{-3}\right) \cdot 2 \]
Calculating this gives:
\[ \Phi_P = \frac{2}{3} \times 10^{-3} \, \text{Wb} \]

### Step 6: Final result
Thus, the magnetic flux through coil P when a current of 2 A flows through coil Q is:
\[ \Phi_P = \frac{2}{3} \times 10^{-3} \, \text{Wb} \approx 0.67 \times 10^{-3} \, \text{Wb} \]