Size of current in parallel wires

[songminho]

Homework Statement

Two parallel wires are positioned at l = 2.76 cm apart. Initially a current I1 = 9.57 A flows up the screen through wire 1, and wire 2 has no current in it.

A current is then sent through wire 2. The magnetic field between the two wires, is found to be 0T.

What is the size of the current flowing through wire 2?

Homework Equations

The Attempt at a Solution

I tried to use

by rearranging to make i the subject:
i = 2pi*rB/μ
= 2pi*0.0276x0/4pix10^-7
then I realized the answer is zero but that is totally incorrect. Am I using the correct formula here? Or should I be using

? (But then here I have 2 unknown variables... F and I2) Help please! Thanks

 

[gneill]

What is meant by "The magnetic field between the two wires"? Is that everywhere between the wires or at some particular location? Is the problem quoted exactly as given to you?

Regardless, you're looking for the net magnetic field B at some location, not the force on another current-carrying wire. Do you have a formula for the magnetic field of a current-carrying wire?

 

[songminho]

What is meant by "The magnetic field between the two wires"? Is that everywhere between the wires or at some particular location? Is the problem quoted exactly as given to you?

Regardless, you're looking for the net magnetic field B at some location, not the force on another current-carrying wire. Do you have a formula for the magnetic field of a current-carrying wire?

yes, that's how the question is worded :/
Is it the formula

? I tried using in the attempt above

 

[gneill]

Since the magnitude of the magnetic field due to a current in a long wire is inversely proportional to the distance from the wire, the location matters. So the question is badly posed. I think the best plan would be to assume that they mean the midpoint between the wires. If that is the assumption, then...

...If the total field is to be zero midway between the wires, what must be the current magnitude and direction in the second wire? Hint: Investigate the Right Hand Rule for magnetic fields around a current-carrying wire.

 

[songminho]

Since the magnitude of the magnetic field due to a current in a long wire is inversely proportional to the distance from the wire, the location matters. So the question is badly posed. I think the best plan would be to assume that they mean the midpoint between the wires. If that is the assumption, then...

...If the total field is to be zero midway between the wires, what must be the current magnitude and direction in the second wire? Hint: Investigate the Right Hand Rule for magnetic fields around a current-carrying wire.

Magnetic field into the screen so current is upwards? Not sure about the magnitude...

 

[songminho]

Magnetic field into the screen so current is upwards? Not sure about the magnitude...

Would the magnitude be the same as wire 1? If they travel in same direction then they attract...?

 

[gneill]

Would the magnitude be the same as wire 1? If they travel in same direction then they attract...?

Attraction or repulsion doesn't play a direct role in addressing the question (although it is a consequence of the interaction of the fields). What is important is the magnitude and relative directions of the parallel currents.

Your conclusion (guess??) about the magnitude of the current is correct, and you should be able to see that it follows from the symmetry of the situation. What is your argument for the current direction though? Did you investigate the right hand rule? If you want the net field to be zero how should the directions of the fields from each wire relate to each other?

 

[songminho]

What is your argument for the current direction though? Did you investigate the right hand rule?If you want the net field to be zero how should the directions of the fields from each wire relate to each other?

The first wire goes up the screen so magnetic field goes into the page. For net field to be zero, it should cancel out? so the 2nd wire also goes up the screen (magnetic field into screen? So the current in the second wire is 9.57A?

 

[gneill]

The first wire goes up the screen so magnetic field goes into the page. For net field to be zero, it should cancel out? so the 2nd wire also goes up the screen (magnetic field into screen? So the current in the second wire is 9.57A?

Yes, that looks good.