Question about two circular concentric coils

[phys62]

Homework Statement

Two circular coils are concentric and lie in the same plane. The inner coil contains 110 turns of wire, has a radius of 0.010 m, and carries a current of 5.6 A. The outer coil contains 190 turns and has a radius of 0.014 m. What must be the magnitude of the current in the outer coil, such that the net magnetic field at the common center of the two coils is zero?

Homework Equations

B=(constant)IN/2R

The Attempt at a Solution

Ok so I have I1=5.6 A
R1=.010 m
N1=110
R2=.014 m
N2=190
I2=?

I think that I have to use that equation somehow and set them equal to each other, but I'm lost after that. Perhaps I'm using the wrong equation entirely? Any help is much appreciated!

Edit: Do I just solve for B1 and then set that equal to the equation for the 2nd coil (only make it negative)?

 

[LowlyPion]

You should be able to figure the magnitude of the field from the first coil from what you're given.

Then they want to know what opposing current using the parameters of the other coil is needed to null out the B field at the center.

I find it easiest to keep it as variables of the 2 loops and then plug in the numbers at the end to solve for the one that you need.

 

[nlightner]

Yes, you are on the right track. Since the two coils are concentric and in the same plane, the net magnetic field at the common center will be the sum of the magnetic fields produced by each coil. The equation you mentioned, B=(constant)IN/2R, is the correct equation to use. However, you need to take into account the direction of the magnetic field produced by each coil.

For the inner coil, the magnetic field will point in the same direction as the current, which is counterclockwise when viewed from the top. So the magnetic field produced by the inner coil will be positive.

For the outer coil, the magnetic field will point in the opposite direction as the current, which is clockwise when viewed from the top. So the magnetic field produced by the outer coil will be negative.

To find the net magnetic field at the common center, you can set the two equations for B1 and B2 equal to each other, since the net magnetic field must be zero. This will give you the magnitude of the current in the outer coil, which you can solve for.

Hope this helps!