A smaller solenoid is placed inside a larger solenoid so they have the same axis

Question

A smaller solenoid is placed inside a larger solenoid so they have the same axis (like concentric cylinders). The inner solenoid has radius r=0.014meters, N=1000turns, and resistance R=13Ohms. Its two leads are connected to an ammeter to form a circuit. The outer solenoid has n=23000turns per meter and carried a current that is increasing ata constant rate of dI/dt=0.5Amperes per second.
What is the current throught the ammeter? What is its direction?
Iinner =

A
Compared to the direction of current through the outer solenoid, the current through the inner solenoid moves in
the same direction.
the opposite direction.

Explanation / Answer

The current through the ammeter is equal to V/R = (df/dt)/R. The field inside the outer solenoid is given by B = µ0In, so df/dt = µ0*dI/dt*n1*a*n2 so I = µ0*dI/dt*n1*pr2*n2/R = (4p x 10^-7)(.5)(23000)*(p(.014)^2)(1000)/13 = 6.84 x 10^-4 amps. Lenz's law dictates that the current in the inner solenoid flows opposite to the current in the outer solenoid.

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