Find the direction of the induced current

[bsmm11]

Homework Statement

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There are two solenoids with their axes parallel, one with a smaller diameter so that it fits inside the other. If the bigger solenoid has a current flowing in the clockwise direction (looked at from above) and the current is increasing in magnitude, find the direction of the induced current in the smaller solenoid.

Homework Equations

The Attempt at a Solution

First, increasing current leads to increasing flux linkage. Then I tried to think that this situation is the same as a smaller solenoid moving upward (●) into the bigger solenoid. Using the right hand grip rule the direction of the magnetic field on the smaller solenoid moving upward is downward (x). (from here I guessed) Since the Lenz's rule is rightly applied, the top of the smaller solenoid is North pole - the current flows in the counter-clockwise.

Well, I got the right answer but I'm not sure about my explanation (especially the guessed part). Could you check my answer?

EDIT: I forgot a very very important question.. The direction I showed are the direction of the magnetic field. But if the direction of the magnetic field is upward or downward, the magnetic(?) force can only be horizontal. That makes things go wrong since the force must be applied upward or downward in this question. I'm getting so confused. What is the right direction of the magnetic field and magnetic force?

 

[gneill]

Check out Lenz's Law and the right-hand rule for solenoids.