Magnetic flux through smaller coil within solenoid

[jdubt]

Homework Statement

A solenoid has 235 turns of wire wrapped along its length of 27 cm. The diameter of the solenoid is 1.5 cm. In the middle of the solenoid is a smaller coil of diameter 1.0 cm with 50 turns of wire along its 2.0 cm length. The two coils are coaxial. A current of 15 A is in the larger solenoid with no current in the smaller coil.
(a) Determine the magnetic flux through the smaller coil.
(b) Determine the mutual inductance of the pair of coils.

Homework Equations

B= mu_not *n*I
flux =B x A

The Attempt at a Solution

I've tried several times with no success. My problem is I don't know how to relate the solenoid to the smaller coil.

B= 4* pi *10^-7*(235/.27)*15 = .01641 T

I believe this is correct but I don't know where to go from here.

flux = (.01641 T)* pi * (.0075)^2

This could be an intermediary step in getting the flux of the smaller coil, but I don't know what to afterwards.

flux = (.01641 T)* pi * (.005)^2

This is incorrect.

Any help would be much appreciated.

 

[Redbelly98]

I agree with your 0.01641 T calculation.

Hmmm ... your flux expression seems right for a single-loop coil, but they give 50 turns for the smaller coil.