KVPY 2019 SB SX Exam Previous Papers

Question : 92 of 120

Marks: +1, -0

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 flows in the short solenoid. Choose the correct statement:

There is uniform magnetic field µ0nI in the long solenoid.
Mutual inductance of the solenoids is πµ0r $^{2}$ nNl.
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 πµ0rRnNlL/(rR) $^{1\/2}$

Validate

Solution:

\f_s = Mi_L

(nl).B_L.πr^2 = Mi_L

nl[µ_0Ni_L] πr ^2 =Mi _ L

M=πµ_0 nNlr^2

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