The mutual inductance `M_(12)` of coil 1 with respect to coil 2

Options

A. increase when they are brought nearer.
B. depends on the current passing through the coils.
C. increases when one of then is rotated about an axis.
D. both (a) and (b) are correct.

Explanation

To solve the question regarding the mutual inductance \( M_{12} \) of coil 1 with respect to coil 2, we can follow these steps:

### Step 1: Understand Mutual Inductance
Mutual inductance is a measure of the ability of one coil to induce an electromotive force (EMF) in another coil due to a change in current. The mutual inductance \( M_{12} \) is defined as the ratio of the magnetic flux linked with coil 1 due to the current flowing in coil 2.

### Step 2: Identify the Relationship
The mutual inductance \( M_{12} \) can be mathematically expressed as:
\[ M_{12} = \frac{N_1 \Phi_{12}}{I_2} \]
where:
- \( N_1 \) is the number of turns in coil 1,
- \( \Phi_{12} \) is the magnetic flux through coil 1 due to the current \( I_2 \) in coil 2.

### Step 3: Analyze Factors Affecting Mutual Inductance
1. **Distance Between Coils**: As the coils are brought closer together, the magnetic flux \( \Phi_{12} \) increases, which in turn increases \( M_{12} \).
2. **Current in Coil 2**: The mutual inductance \( M_{12} \) also depends on the current \( I_2 \) flowing through coil 2. A change in \( I_2 \) will affect the induced EMF in coil 1.

### Step 4: Conclusion on Statements
Based on the analysis:
- The mutual inductance \( M_{12} \) increases when the coils are brought closer (true).
- The mutual inductance \( M_{12} \) depends on the current \( I_2 \) flowing through coil 2 (true).
- Therefore, both statements regarding the behavior of mutual inductance are correct.

### Final Answer
Both statements A and B regarding the mutual inductance \( M_{12} \) of coil 1 with respect to coil 2 are correct.

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