Magnetic Force problem

[eku_girl83]

Three parallel wires each carry current I in the direction shown in the figure (file attached). If the separation between adjacent wires is d, calculate the magnitude and direction of the net magnetic force per unit length on each wire.
a) What is the magnetic force on the top wire?
I think the direction is up, but I don't know how to find the magnitude.
b) What is the magnetic force on the middle wire?
I know this is zero
c) What is the magnetic force on the bottom wire?

I also know that net magnetic force per unit length is equal to (mu0*I*I')/(2*pi*r).
mu0=4*pi*10^-7

Any help would be appreciated!!!

[Doc Al]

Originally posted by eku_girl83
a) What is the magnetic force on the top wire?
I think the direction is up, but I don't know how to find the magnitude.
The top wire will experience the net force due to each of the other two wires. Treat each pair separately and add up the forces.

If the current goes in the same direction, the wires will attract; if the opposite direction, they repel. So, the middle wire exerts an upward force on the top wire. (To find the magnitude, use your formula.) And the bottom wire exerts a downward force on the top wire. (Find the magnitude.) Now just add these forces up, remembering that they are vectors.

Since the middle wire is closer, it exerts the greater force. So the net force will be upward, as you predicted.


b) What is the magnetic force on the middle wire?
I know this is zero
Right.
c) What is the magnetic force on the bottom wire?
Realize that, by symmetry, the force on the top wire must equal the force on the bottom wire, but point in the opposite direction.
I also know that net magnetic force per unit length is equal to (mu0*I*I')/(2*pi*r).
mu0=4*pi*10^-7

Good. Now use it, one pair at a time.