1. Oct 7, 2009

### Skye77

A circular wire loop with a diameter of 0.2m and a long, straight wire carry currents, I(1) AMP and I(2) AMP, respectively. Both wires are located in the plane of the page, and the distance between the long wire and the center of the circle is 0.15m.

What is the magnitude of I(1) if the magnetic field at point O is zero when I(2) = 3 AMP?

Here's where I get stuck. I know that I'm supposed to use the equations:
B= μ0*I/2*pi*d
and
B= μ0*N*I/2*r

I re-arranged the equations to figure out that to solve for I(1) it would be
I(1)= B*2*r/μ0N

N = 1, since it's a single loop
r = .1m
μ0 = 4*pi*10^-7

I think I'm supposed to solve B from the straight wire equation, so I re-arranged that equation to: I(2) = B*2*pi*d/μ0

I(2) = 3 AMP
d = .15m
etc...

But the question asks: what is the magnitude of I(1) if the magnetic field (B) at O is zero when I(2) = 3 AMP

Does that mean the answer would also be zero? How then would I determine direction of
I(1)? Clock-wise or Anti-clockwise?

Thanks.

File size:
3.2 KB
Views:
111
2. Oct 7, 2009

### rl.bhat

You need not take into account of the direction of the curents in the straight wire and the circular loop.
Find the field at the center of the circular due to straight wire and the circular loop, and equate them to find I1.

3. Oct 7, 2009

### Skye77

So, the field at the center of the circular loop due to the straight wire is zero when the current is 3 AMPs. How do I go from there to determine the current at I(1) - the loop?

I guess I don't understand what you mean by equating them.

4. Oct 7, 2009

### rl.bhat

B= μ0*I1/2*pi*d
and
B= μ0*N*I2/2*r

These two equations which you have written, together produce zero magnetic field at the center of the circular loop. I2 is given. Find I1

5. Oct 7, 2009

### Skye77

I think I have a mental block on this, but here's what I've done based on what you said...

For the straight wire: B = μ0*I1/2*pi*d
I plugged everything in and calculated B = 4 x 10-6

Then do I use that B in the second equation: B= μ0*N*I2/2*r to solve for I?

I don't get a round number, which I expected to get.

I also tried doing I1 + I2 = 0, and by that I would get a -3 Amp which would make the current direction on the circle switch directions to counterclockwise?

Am I getting any closer?

6. Oct 7, 2009

### rl.bhat

At the center of the coil magnetic field due to wire and loop must be equal and opposite.

B= μ0*I1/2*pi*d = μ0*N*I2/2*r
Substitute the values of d, r and I2, and find I1.