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Two circular coils can be arranged in three ways: (i) coaxially with planes parallel (facing each other), (ii) coplanar (in the same plane), (iii) with axes perpendicular to each other. In which arrangement is the mutual inductance maximum?

1. maximum in situation (i)
2. maximum in situation (ii)
3. maximum in situation (iii)
4. the same in all situations

Correct answer: maximum in situation (i)

Solution

Mutual inductance M = (flux through coil 2 due to coil 1) / (current in coil 1). When the two coils are coaxial (situation i), the magnetic field from one coil passes entirely and normally through the other coil, maximising flux linkage. In situation (ii) (coplanar), the field lines of one coil pass through the plane of the other at oblique angles reducing net flux. In situation (iii) (axes perpendicular), the flux from one coil through the other is zero by symmetry (M = 0). Hence mutual inductance is maximum in situation (i).

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