Physics · Electromagnetic Induction · NEET
No. If you drive coil 1 with current I₁, it links flux N₂Φ₂ through coil 2, and M₂₁ = N₂Φ₂ / I₁. If instead you drive coil 2 with I₂, it links N₁Φ₁ through coil 1, and M₁₂ = N₁Φ₁ / I₂. These two numbers come out exactly equal: M₁₂ = M₂₁. The coupling depends only on the geometry (size, shape, number of turns, separation, orientation) and the medium — not on which coil is the source. So swapping the source coil does not change M.
Because M₁₂ = M₂₁, both directions give the same value, so we just call it M. This is the reciprocity theorem. It saves work: whichever coil is easier to treat as the source, you compute that M, and it is automatically the M for the reverse case too. For NEET, this is why a problem tells you 'the mutual inductance of the pair is M' without saying which coil is driven.
The deep reason is energy. The energy stored in the shared magnetic field of two coupled coils is U = ½L₁I₁² + ½L₂I₂² + M I₁I₂. The final field energy cannot depend on the ORDER in which you switch the currents on. Building I₁ first then I₂, versus I₂ first then I₁, must give the same total energy. Working that out forces the cross-term coefficient to be a single M in both cases, which means M₁₂ must equal M₂₁. It is conservation of energy, not a coincidence.
It always holds for any two coils in a linear medium (air, vacuum, or a material whose permeability does not depend on current, like a non-saturated core). M₁₂ = M₂₁ is a general theorem. It can appear to break only with strongly non-linear ferromagnetic cores near saturation, which is outside the NEET Class 12 syllabus. For every NEET problem, treat M₁₂ = M₂₁ as always true.
That is the whole practical value of reciprocity. Take two coaxial solenoids: finding the flux the inner one produces in the outer is hard, but the outer's field is uniform and easy to use for the flux through the inner. Because M₁₂ = M₂₁, the M you get the easy way is the same M for the hard direction. In the 2021 coplanar-loops PYQ, you treat the big loop as the source (its field at the centre is simple) even if the small loop is actually driven — reciprocity guarantees the answer is right.
Two conducting circular loops of radii R₁ and R₂ are placed in the same plane with their centres coinciding. If R₁ >> R₂, the mutual inductance M between them will be directly proportional to:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Yes. Even if coil 1 has 1000 turns and coil 2 has 5 turns, M₁₂ = M₂₁ exactly. The turn counts and geometry are baked into the single value M; the equality does not require the coils to be identical.
The henry (H), the same unit as self-inductance. One henry means an emf of 1 volt is induced in the second coil when the current in the first coil changes at 1 ampere per second: 1 H = 1 V·s/A = 1 Wb/A.
It lets you always choose the source coil whose magnetic field is easiest to write down (uniform, symmetric). You compute M once from that easy side, and the answer is valid for either coil being driven. This turns many hard flux calculations into simple ones.
No, as long as the medium is linear (air, vacuum, or an unsaturated core). M depends only on geometry, turns, separation, orientation, and the permeability of the medium — not on the magnitude of the current.
Self-inductance L links a coil's own changing current to the emf in that SAME coil. Mutual inductance M links a changing current in one coil to the induced emf in a DIFFERENT coil. Reciprocity (M₁₂ = M₂₁) is a special property of mutual inductance between the pair.
