Question

Two coils are placed closed to each other. The mutual inductance of the pair of coils depends upon the :

• A. rate at which currents change in the two coils.
• B. relative position and orientation of the coils.
• C. currents in the two coils.
• D. value of voltage induced in one coil due to change in value of current in the other coil.

Hint:

Inductance ($L$ or $M$) is like electrical inertia or capacitance $C$: it depends purely on geometry, dimensions, material medium, and alignment, NOT on instantaneous current, voltage, or rate of current change.

Answer 1

The Correct Option is B

Concept:
• Mutual inductance $M$ represents the magnetic coupling between two coils, defined by $\Phi_2 = M I_1$.

• $M$ is purely a geometric constant determined by physical construction and arrangement of the coils.

Step 1: Analyze dependence of mutual inductance
Mutual inductance $M$ depends on:
1. Number of turns $N_1$ and $N_2$ in the two coils.
2. Cross-sectional areas $A_1$ and $A_2$ and lengths of the coils.
3. Relative distance/separation between coils.
4. Relative spatial orientation and alignment of their axes (coupling coefficient $K$).
5. Magnetic permeability $\mu$ of core material inside coils.

Step 2: Eliminate incorrect options
$M$ is independent of current $I$, rate of change of current $\frac{dI}{dt}$, or induced electromotive force $e$.
These quantities determine induced voltage ($e = -M \frac{dI}{dt}$), but do not affect the fundamental geometric constant $M$ itself.

Step 3: Conclusion
Mutual inductance depends on relative position and orientation of the coils, corresponding to option (B).