Mutual Inductance Of Two Coaxial Solenoids — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Mutual Inductance of Two Coaxial Solenoids Valid for two long coaxial solenoids of equal length where the length is much greater than the radius (l >> r). Assumes an air core (or vacuum). Assume a current I 2 flows through the outer solenoid, creating a magnetic field B 2 = 0 n 2 I 2. This magnetic field passes through the cross-sectional area of the inner solenoid, A = r 1 2. The magnetic flux through one turn of the inner solenoid is 1 = B 2 A = 0 n 2 I 2 r 1 2. The total flux linkage with the inner solenoid (having N 1 = n 1 l turns) is 1 = N 1 1 = (n 1 l)( 0 n 2 I 2 r 1 2). Using the definition of Mutual Inductance M = 1 / I 2, we divide by current I 2. Result: M = 0 n 1 n 2 r 1 2 l. The solenoids must be long (l >> r) to ignore end effects. The magnetic field is assumed uniform inside the inner solenoid and zero outside the outer solenoid. Assumes 100% flux linkage (ideal coupling) over the area of the inner solenoid. Confusion between total turns (N) and turns per unit length (n). Formula changes to M = 0 N 1 N 2 A / l if N is used. Using the radius of the outer solenoid (r 2) instead of the inner solenoid (r 1) for area calculation. Flux is only linked effectively through the inner core area. Believing Mutual Inductance depends on the current flowing through the coils (it is a geometric constant).