Two circular coils have their centres at the same point. The mutual inductance between them will be maximum when their axes

Options

A. Perpendicular to each other
B. At `60^(@)` to each other
C. At `45^(@)` to each other
D. Parallel to each other

Answer

To solve the problem of determining the orientation of two circular coils that maximizes their mutual inductance, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Mutual Inductance**:
- Mutual inductance (M) between two coils is a measure of how much magnetic flux from one coil links with the other coil. It is influenced by the relative orientation of the coils.

2. **Visualizing the Coils**:
- Imagine two circular coils with their centers at the same point. We can visualize them in different orientations: parallel, perpendicular, or at angles to each other.

3. **Analyzing Parallel Orientation**:
- When the axes of the two coils are parallel to each other, the magnetic field lines produced by the primary coil will pass through the secondary coil effectively. This results in a maximum number of magnetic field lines linking the two coils.

4. **Magnetic Flux Linking**:
- The magnetic flux (Φ) linked with the secondary coil due to the primary coil can be expressed as:
\[ Φ_2 = M \cdot I_1 \]
where \(Φ_2\) is the magnetic flux linked with the secondary coil, \(M\) is the mutual inductance, and \(I_1\) is the current in the primary coil.

5. **Maximizing Magnetic Flux**:
- Since mutual inductance is directly proportional to the magnetic flux linked with the secondary coil, to maximize \(M\), we need to maximize \(Φ_2\). This occurs when the coils are aligned parallel to each other.

6. **Conclusion**:
- Therefore, the mutual inductance between the two coils will be maximum when their axes are parallel to each other.

### Final Answer:
The mutual inductance between the two circular coils will be maximum when their axes are **parallel to each other**.