Recall the definition of mutual inductance

If two coils are placed near each other, a current in one coil produces magnetic flux through the other coil. The mutual inductance $M$ is defined by

where:

• $I_1$ = current in coil 1,
• $\Phi_{21}$ = magnetic flux through coil 2 due to coil 1,
• $N_2$ = number of turns in coil 2.

Also, induced emf in coil 2 is

What factors does mutual inductance depend on?

Mutual inductance depends on the magnetic coupling between the two coils. This is determined by:

• number of turns,
• size and shape of coils,
• medium between them,
• relative position and orientation of the coils.

Evaluate each option

A: the rates at which currents are changing in the two coils

This affects the induced emf because

but it does not determine the value of $M$ itself.

So, A is incorrect.

B: relative position and orientation of the two coils

If the coils are moved farther apart or rotated, the magnetic flux linkage changes, so mutual inductance changes.

Thus, B is correct.

C: the currents in the two coils

For linear media, mutual inductance is a geometrical/property constant of the arrangement and does not depend on the actual current values.

So, C is incorrect.

D: the materials of the wires of the coils

Mutual inductance depends on magnetic coupling, not on whether the wire is copper, aluminum, etc. Wire material mainly affects resistance, not mutual inductance.

So, D is incorrect.

Final answer

The mutual inductance depends upon the relative position and orientation of the two coils.

Therefore, the correct option is:

Comparison with stored correct answer

Stored correct answer: B

My derived answer: B

They match.