Two circular coils of radius 10 cm and 15 cm are placed close to each other. Current of 0.2 A flows through the coil of radius 10 cm. Find the flux linked with coil of 15 cm if coefficient of mutual inductance of the pair is 0.005 H.

Answer

To solve the problem, we need to find the magnetic flux linked with the coil of radius 15 cm due to the current flowing in the coil of radius 10 cm. We will use the formula for mutual inductance.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Radius of coil 1 (R1) = 10 cm = 0.1 m
- Radius of coil 2 (R2) = 15 cm = 0.15 m
- Current (I) flowing through coil 1 = 0.2 A
- Coefficient of mutual inductance (M) = 0.005 H

2. **Understand the Formula for Flux Linked:**
The flux (Φ) linked with coil 2 due to the current in coil 1 can be calculated using the formula:
\[ \Phi = M \times I \]
where:
- Φ is the magnetic flux linked with coil 2,
- M is the mutual inductance,
- I is the current flowing through coil 1.

3. **Substitute the Values into the Formula:**
Now we can substitute the known values into the formula:
\[ \Phi = 0.005 \, \text{H} \times 0.2 \, \text{A} \]

4. **Calculate the Flux:**
Performing the multiplication:
\[ \Phi = 0.005 \times 0.2 = 0.001 \, \text{Wb} \]

5. **Convert to Standard Form:**
To express the result in standard form:
\[ \Phi = 1 \times 10^{-3} \, \text{Wb} \]

### Final Answer:
The flux linked with the coil of radius 15 cm is \( 1 \times 10^{-3} \, \text{Wb} \).

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