Q.The mutual inductance $M_{12}$ of coil 1 with respect to coil 2

Mutual inductance is set by the geometry of the pair of coils — their number of turns, size, separation, orientation and the medium — not by the current they carry. Bringing the coils nearer increases the flux linkage per unit current, so $M$ increases. By the reciprocity theorem the coupling is symmetric, $M_{12}=M_{21}$. Rotating one coil about an axis reduces the shared flux, so it lowers …

Concept understanding

For two coils, $M_{12}=\dfrac{N_1\Phi_{12}}{I_2}$. Although the current $I_2$ appears in the definition, $M$ itself is a ratio of flux linkage to current and is fixed by the fields' geometry: the turns $N_1,N_2$, the coil dimensions, the distance and orientation between them, and the permeability of the medium. The value of the current cancels out.

Testing each option

• (a) Bringing the coils nearer means more of coil 2's magnetic flux threads coil 1, so the flux linkage per unit current — and hence $M$ — increases. True.
• (b) claims $M$ depends on the current. False — $M$ is a geometric property; the flux is proportional to the current, so their ratio is current-independent. …

Method: Evaluating Claims About Mutual Inductance M

Use this checklist for any MCQ that tests properties of the mutual inductance between two coils — what it depends on, how it responds to geometric changes, and whether it's symmetric.

Steps

Step 1: Recall the defining relation, and notice what actually survives in it

Although the current $I_2$ appears explicitly, the flux $\Phi_{12}$ it produces is itself directly proportional to $I_2$ — so the ratio $M_{12}$ is independent of the current's actual value. Any option claiming "$M$ depends on the current" is false purely from this algebraic cancellation, without needing any specific numbers.

Step 2: Recall what M genuinely depends on — geometry only

$M$ is fixed by the number of turns, the coils' sizes and shapes, their separation, their relative orientation, and the permeability of the medium between them. Use this to judge any geometric-change claim:

• Coils brought closer together → more of one coil's flux threads the other per unit current → $M$ increases.
• A coil rotated away from alignment with the other → less shared flux → $M$ decreases (a claim that rotation always increases $M$ is false — it's maximum only at the aligned/coaxial orientation and falls off as the coils are turned away from it).

Step 3: Recall the reciprocity theorem …