Which Direction Will the Induced Current Flow?

[Biker]

Homework Statement

After you close the switch, There will be an induced current in the resistance R, Choose one of the following:
Direction of current ... magnitude of current
A to B ... decreasing
A to B ... increasing
B to A decreasing
B to A... Increasing

Homework Equations

Faraday's law
lenz's law

The Attempt at a Solution

When you close the switch a current in the counter clockwise direction flows in the black circuit thus a magnetic field is created inside the solenoid pointing to the right and increasing with time.

Now the red circuit will produce a magnetic field in the other direction, which means the current will be from B to A and decreasing

However, the book disagrees( well old exam) It says that it will flow from A to B and decreasing.

 

[J Hann]

Since Lenz' Law says that an emf is set up opposing the cause producing it, what if you
replace the inductors by emf's?
Also, the flux in the secondary circuit will tend to decrease the flux in the primary circuit
if you look at the flux thru the two coils.

 

[Biker]

Since Lenz' Law says that an emf is set up opposing the cause producing it, what if you
replace the inductors by emf's?
Also, the flux in the secondary circuit will tend to decrease the flux in the primary circuit
if you look at the flux thru the two coils.

Well isn't the primary circuit creating a magnetic field that is pointing to the left.
Now there is an increasing magnetic field pointing to the left in the secondary coil, It will try to oppose it.
It will creating a magnetic field pointing to the right

Thus the current is from B to a

Edit: Found a paper that changed the answer to my answer.. Thanks

 

[J Hann]

Another way to look at this is that by Lenz' Law the inductor in circuit 1 will generate a back Emf
that will oppose the Emf at the switch (positive at the left side of the inductor).
The same thing happens in the parallel circuit - it must also the oppose the change in flux taking place
in that circuit creating an Emf with the A side positive with respect to B.
Trying to analyze the flux changes can be a bit confusing.
When the switch is closed the rate of change in flux must be a maximum because the current in the
first circuit is zero because the back Emf equals the Emf generating the current in circuit 1.
As the back Emf decreases in circuit 1 the current increases.
The back Emf also decreases in circuit 2 so the current decreases.