Induced current of a coil on another coil

[dumbdumNotSmart]

Homework Statement

We have two coils of copper wire, drawn below. One has a battery connected to it. The other one has a galvonometer connected. If the coil with the voltage is moved closer as shown in the picture, with considerable velocity, what direction will the current induced on the other coil have? The coils are stacked towards the viewer, they are drawn in an escalating manner for clarity. Help me understand why what happens, happens.

Homework Equations

Right hand rule
Faraday-Lenz

The Attempt at a Solution

First I thought the other coil was going to oppose the rise in magnetic field on the outside, thus the following made sense to me.

However, the following reasoning also seems valid: The coil will most oppose the rise in magnetic field on the inside if the wires are considered virtually dimensionless and perfectly stacked. Then the direction of the current will have the opposite direction.

According to the solutions handbook, the current flows towards the left on the galvanometer and since my knowledge is very limited to just mechanical solving of magnetic fields, I thought I'd ask you guys to cultivate some knowledge on the theory of induction.

 

[Charles Link]

You get an increased magnetic flux from the first circuit onto the second circuit. A voltage gets established in the second circuit by Faraday's law that will generate a current. The magnetic field from this generated current will be in such a direction as to try to keep the magnetic flux from changing nearly as much.

 

[dumbdumNotSmart]

You get an increased magnetic flux from the first circuit onto the second circuit. A voltage gets established in the second circuit by Faraday's law that will generate a current. The magnetic field from this generated current will be in such a direction as to try to keep the magnetic flux from changing nearly as much.

Alright, I agree with everything you said! However, it still does not answer my question. You've seen my work, so you know I'm having trouble thinking of where the induced flux will go against the flux generated by the first coil. It does not seem to make sense to me that the second solution I presented would be the correct one. If there is an intense flux left of the second coil, the seemingly logical answer would be that a current would be induced so that the induced flux went in the opposite way of the flux being generated by the first coil. Hence: Solution 1?

 

[Charles Link]

I agree with your solution #1. You have the original loop that makes a clockwise current. This has a (correctly drawn) magnetic field into the paper inside the loop and magnetic field out of the paper outside the first loop. A clockwise current in the second loop will cause a magnetic field into the paper inside this second loop (just as in the first ; clockwise is into paper), and will oppose the change that takes place of an increasing magnetic field out of the paper from the first loop. (It is assumed the loops do not overlap).

 

[dumbdumNotSmart]

I agree with your solution #1. You have the original loop that makes a clockwise current.

I am slightly confused, my solution 1 has a counterclockwise current. You mention having the flux of the induced current go into the paper in the center of the first coil, so as to counteract the change in flux... but this would mean adding more magnetic field lines into the paper where they are increasing.

I think it's convenient to think this another way: There is an A coil with a voltage approaching the B coil. There are two directions the current can be induced. Which direction will the current have in coil B so as to not generate infinite energy?

Now you bring up your trusty partner, O' right hand rule, tell me how the current goes. Point your index finger in the direction of the current (point nearest to coil B), and your thumb in the direction of the force of the magnetic field so as to not generate infinite amounts of energy (we don't want masses approaching each other at light speeds, how inconvenient would that be in the real world!) this direction would be contrary to the velocity of the coil. The direction of your middle finger is the direction of the INDUCED magnetic field. Aha, it means that the induced magnetic field goes upwards! Therefore, solution 2, no?

 

[dumbdumNotSmart]

I'm sorry I'm changing my mind so often, but your answer swept a wave of realization over me.

 

[Charles Link]

Your diagrams were somewhat hard to follow-I may have misinterpreted the direction of the current flow in your diagrams. In any case, the explanation I gave should tell you the correct result. Note, the magnetic field out of the paper from the first loop "into" (i.e.= out of the paper through) the second gets stronger as the loops get closer together. The current generated in the second loop will be clockwise to generate a magnetic field that opposes this change. The magnetic field from this generated current will be into the paper inside the second loop.