Circuits and Direction of Magnetic Field

[diabolical]

Homework Statement

Consider the portion of a circuit shown in the figure. When no current is running, both compasses point north (direction shown by the pale arrows). When current runs in the circuit, the needle of compass 1 deflects as shown. The wire is on top of the compass.

Which statements are true about the direction of the needle of compass 2?

1. It will deflect the same amount as compass 1.
2. It will switch direction and point towards the lower left.
3. It will point upward just as much as compass 1.
4. It will switch direction and point towards the upper left.
5. It will deflect less than compass 1 since the current has been used up.
6. It will not deflect at all.Which direction does the current flow?

1. counterclockwise
2. clockwise

Homework Equations

Right-Hand Rule I guess.

The Attempt at a Solution

I successfully got the second part of the question (direction of current) to be counterclockwise.

The hiccup I am having is with the first part. So far I've tried:
1 & 4
1, 3 & 4
4 & 5
3, 4 &5

All of them are wrong, but I guess this is more of a conceptual question. Would the needle deflect less cause the current is used up more? At first I thought no, because in my head a current can't be used up, but I may be wrong. And what does "It will point upward just as much as compass" even mean?

Thanks in advance!

*edit* added compass number for clarity

 

[Stonebridge]

I think there is a misprint in this question.
Firsly, I think the statements should read "as much as compass 1".

As the current is in the opposite direction (L to R)over compass two, it will be deflected upwards. The magnetic field is in the shape of concentric circles around the wire.
The result will be that it points towards the upper right right.
If all other things are equal (distance of compass from wire, strength of compass needle magnet) then the amount of deflection of compass 2 upwards will be equal to the amount of deflection of compass 1 downwards. This is because the current will be the same in all parts of the wire.

As for which answers are correct - my opinion is that either this is a very poor question, or there are parts missing from the statements, or both.
I'm guessing they intend 3 to be correct, though it should read "It will deflect upwards as much as compass 1 deflects downwards"
They may also want you to say statement 1 is correct. The amount of deflection of 1 is equal to the amount of deflection of 2. But as they are in different directions, one could argue that the actual angle of deflection is not the same. One is, say +20 degrees and the other -20 degrees. One is due west and the other due east.
2,4,5 and 6 are all wrong, by the way.

My view is that whoever wrote this question, assuming it is printed here as it was written, needs either a refresher course in pedagogics or a decent word processor.

 

[diabolical]

I completely agree with you.

I am a bit confused on the direction part though. (why 4 is wrong). If we consider the right hand rule, the magnetic field due to the wire at compass 2 would be in the opposite direction as that of compass 1 correct? Now, if we factor in that the magnetic field strength only caused a deflection of ~20 degrees to compass 1 to the top right, wouldn't a magnetic field in the opposite direction cause a ~20 degree shift to the top left(4)?

Or is my orientation completely messed up in terms of the top-left/top-right aspect?

 

[Stonebridge]

The compass needles will always want to point north - to the right in the diagram.
I assume this is just due to the Earth's field and it's what compass needles usually due when left alone.
To this force is added the component due to the current in the wire.
In one case this is due east, and the other due west.
The largest possible deflection for the needles would be fully due East or fully due West. This would be the case where the field due to the wire was very much stronger than the Earth's field.
In order for the needles to "flip" and point to the left, the Earth's field would have to reverse and also point to the left. (Due south)

 

[rwisz]

The correct answer is 4. It will switch direction and point towards the upper left.

This is because the direction of the magnetic field created by the current in the wire is perpendicular to the plane of the compass. When current is running, the needle of compass 1 deflects in a direction determined by the right-hand rule (pointing towards the upper left). Since compass 2 is also in the plane of the wire, it will experience a force in the opposite direction, causing it to deflect in the opposite direction as compass 1 (pointing towards the upper left).

The statement "It will point upward just as much as compass 1" is incorrect because the direction of deflection is not determined by the strength of the current, but rather by the direction of the magnetic field. Therefore, compass 2 will deflect in the same direction as compass 1, but not necessarily the same amount.

The statement "It will deflect less than compass 1 since the current has been used up" is also incorrect. The current is not "used up" in a circuit, it flows continuously. The deflection of the compass needle is determined by the strength of the magnetic field, not the amount of current.