A short solenoid (length l and radius r with n turns per unit length) lies well inside and on the axis of a very long, coaxial solenoid (length L , radius R and N turns per unit length, with R r ). Current I follows in the short solenoid. Choose the correct statement.

Question

A short solenoid (length l and radius r with n turns per unit length) lies well inside and on the axis of a very long, coaxial solenoid (length L , radius R and N turns per unit length, with R > r ). Current I follows in the short solenoid. Choose the correct statement., There is uniform magnetic field μ 0 n I in the long solenoid., Mutual inductance of the solenoids is π μ 0 r 2 n N l ., Flux through outer solenoid due to current I in the inner solenoid is proportional to the ratio R / r ., Mutual inductance of the solenoids is π μ 0 r R n N l L / r R 1 / 2 .

MARKS App · Accepted Answer

We use reciprocatory theorem to calculate mutüal inductance of the system of solenoids. Let outer solenoid carries a current I 1 . Flux linked with small solenoid 2 is proportional to the current in large solenoid 1 . ⇒ ϕ 21 ∝ I 1 ⇒ n l μ 0 N I 1 π r 2 ∝ I 1 Proportionality constant is the coefficient of mutual inductance M of system. Note that M 12 = M 21 in all cases. So, n / μ 0 N l 1 π r 2 = M l 1 or M = π r 0 r 2 n N I

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