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 (lengthL, radius R and N turns per unit length, with R>r). Current I flows in the short solenoid. Choose the correct statement

Options

A. There is uniform magnetic field `mu_0nI` in the long solenoid
B. Mutual inductance of the solenoids is `mu_0r^2nNl`
C. Flux through outer solenoid due to current I in the inner solenoid is proportional to the ratio R/r.
D. Mutual inductance of the solenoids is `pimu_0rRnNlL(rR)^(1//2)`