Question

The mutual inductance of a pair of coils placed close to each other depends upon

• A. The rate at which currents are changing in the two coils.
• B. Relative position and orientation of the two coils
• C. The materials of the wires of the coils
• D. The current in the two coils

Hint:

\(M=\phi_2/I_1\) is a geometric quantity.

Answer 1

The Correct Option is B

Step 1: Start from the definition.
Flux in coil 2 due to coil 1 is \(\phi_2 = M I_1\), so \(M = \phi_2 / I_1\).

Step 2: What decides M.
Both \(\phi_2\) and \(I_1\) grow together, so their ratio is fixed by the layout: gap, alignment, turns, area and core medium.

Step 3: Rule out the rest.
Rate of change of current, the current itself and the wire metal do not appear in this ratio. Hence only relative position and orientation matter, which is option 2.

Final Answer:
Only the relative position and orientation of the coils matter, option 2. \[ \boxed{\text{Option 2}} \]