# Induced current through a resistor - with variable resistor and two coils

## Homework Statement

The two solenoids in the figure are coaxial and fairly close to each other.
While the resistance of the variable resistor in the left-hand solenoid is increased at a constant rate, the induced current through the resistor R will

A - flow from a to b.
B - flow from b to a.
C - be zero because the rate is constant.

## Homework Equations ## The Attempt at a Solution

I recall something about Lenz Law stating if the current is constant there will be no induced emf, so C is not correct.

If the current is increasing the emf is opposite to I. If the current is decreasing the emf is in same direction as I.

I cannot find anything in my book about this variable rersistor and am having a hard time with this right hand rule for induced current.

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Redbelly98
Staff Emeritus
Homework Helper
Start by thinking about what happens to the current (and therefore the magnetic field) in the coil on the left.

The current will flow from left to right correct? and magnetic field into the page?

this new right hand rule has me off. I am to place my thumb in direction of B and curl my fingers into the induced I? therefore the current on coil 1 will flow in a clockwise direction?

Redbelly98
Staff Emeritus
Homework Helper
The current will flow from left to right correct? and magnetic field into the page?
Correct on the current. As for the magnetic field: look at how the current is flowing through the coil. The magnetic field will be either to the left or right, not into/out of the page.

current to the right and magnetic field going to the left. right?

if this is true (what i posted above here) then would the current in coil loop two flow from b to a?

Redbelly98
Staff Emeritus
Homework Helper
current to the right and magnetic field going to the left. right?
Yes.

... would the current in coil loop two flow from b to a?
You've made a big jump without explaining any intermediate steps.

How does B change, given what Rvar is doing? I.e., in what direction is the change in B? (left or right?).

Once you figure that out, you can use Lenz's Law to figure out the direction of the induced current for the right-hand coil and resistor.

honestly i do not know. i was going on the flow of the current in coil (left) and assuming it went from a to b.

i do not know anything about the Rvar. What does it do?

i am not 100% sure how the current in one and two flows to the right. i just looked at the coils and saw its direction, plus the positive side of the battery. I can tell the current should flow in the same direction on each coil.

how does the Rvar have anything to do with coil 2? coil one is creating an induced current on coil 2 but that should be created regardless of the Rvar right? The Rvar should/could not create a negative current; therefore changing the currents direction, so i think the Rvar should not have much of an impact on coil 2 for these reasons?
The only thing I can see the Rvar is doing is changing the current in coil 1.

help?

edit - thinking about Lenz's Law - it tries to keep the magnetic field constant = no change. in order for that to happen we need a B on coil 2 in the right direction. for that to happen we need a current to the right. which would give me flow from b to a.

i still do not know anything about Rvar

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this is due by noon today. please.

Redbelly98
Staff Emeritus
Homework Helper
From the original post:

... the resistance of the variable resistor in the left-hand solenoid is increased at a constant rate ...

if resistance is increased then the current (I) is decreased correct? I= V/R

if the current is decreased in coil 1 then the B of coil 2 is decreased as well right? decreasing B filed to the left.

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Redbelly98
Staff Emeritus
Homework Helper
Not sure if you're still trying to work this one out, but:

if resistance is increased then the current (I) is decreased correct? I= V/R
Yes.

if the current is decreased in coil 1 then the B of coil 2 is decreased as well right? decreasing B filed to the left.
Yes, B (which points to the left) of coil 2 decreases.

So the direction of dB/dt is _____ ?

Or, asked another way ... suppose for example B changes from -3 Tesla (i.e., 3 Tesla, to the left) to -2 Tesla. The change in B is ____ Tesla, towards the _____ (right/left)?

Not sure if you're still trying to work this one out, but:

Yes.

Yes, B (which points to the left) of coil 2 decreases.

So the direction of dB/dt is _LEFT____ ?

Or, asked another way ... suppose for example B changes from -3 Tesla (i.e., 3 Tesla, to the left) to -2 Tesla. The change in B is _1___ Tesla, towards the _right____ (right/left)?

i filled in above.

here is what was I got from class tonight.

we have a current to the right and B to the left on coil 1. with the variable resistor it is decreasing I which in turn is decreasing B. If we have to "oppose" a decreasing B then the B of coil 2 needs to be to the left as well. (to ADD to the decreasing B currently) in order for this to happen the I on coil 2 must be to the right, therefore flowing from B to A.

correct?

Redbelly98
Staff Emeritus
Homework Helper
Yes.

my reasoning sound correct also?

thanks for all your help! with me knowing the directions on coil 1 it made it easier to explain what I needed coil 2 to have

Redbelly98
Staff Emeritus