Physics Question?

Question

I'm having quite a bit of trouble setting this problem up. I know I need to use the equation B= [(4pi x 10^-7)(current)]/(2pi x radius), for both A and B and add to get the magnitudes, but I have no idea what numbers to plug (i.e. the radius) to get 2 equations for each to add. Can anyone offer me some guidance/assistance? Thanks in advance.

Two long, straight wires are separated by 0.12 m. The wires carry currents of 5.5 A in opposite directions, as the drawing indicates.

http://www.webassign.net/CJ/21_56.gif

a) Find the magnitude of the net magnetic field at the point A. (in T)

(b) Find the magnitude of the net magnetic field at the point B. (in T)

Answer 1

The radius is the distance from the point to each wire.

Answer 2

a) Use B = 2 E-7 I/s, where s stands for distance from point to wire, for BOTH currents. Note s is 0.03 for the nearer wire, and 0.15 for the other.

B = 2 E-7 × 5.5 (1/0.03 - 1/0.15) = 2.9333 E-5 T.

Or, you can obtain the same result applying superposition: Total field intensity is the (algebraic) sum of the field set up by one current plus the field set by the farther current. You'll get the same result. Observe that fields oppose each other, since currents flow in opposite direction. Cancellation is partial only, because distance form point a to wires isn't the same.

b) From inspection, B = 0 at this point. Since point B is equidistant to both wires, and current is the same for both wires, both fields cancel completely. There shouldn't be any need to demonstrate this. Anyhow, if you're not convinced, just go ahead and compute the resultant field by formula.