How Does Current Direction Affect Magnetic Force Between Parallel Wires?

[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.

 

[M98Ranger]

a) To find the magnitude of the magnetic force on the top wire, we can use the formula for the net magnetic force per unit length. In this case, the current in the top wire is I and the current in the adjacent wire is also I, so we can plug these values into the formula and solve for the magnitude:

F = (mu0*I*I')/(2*pi*d)

Where mu0 is the permeability of free space (equal to 4*pi*10^-7), I is the current in the top wire, and I' is the current in the adjacent wire. In this case, both I and I' are equal to I, so we can simplify the formula to:

F = (mu0*I^2)/(2*pi*d)

Now, we just need to plug in the value for d, the separation between the wires, to find the magnitude of the magnetic force on the top wire. The direction of the force will be upward, as you correctly stated.

b) The magnetic force on the middle wire will indeed be zero. This is because the current in the adjacent wires is flowing in opposite directions, and the magnetic forces from these currents will cancel out, resulting in a net force of zero on the middle wire.

c) To find the magnetic force on the bottom wire, we can use the same formula as in part a, but this time the current in the adjacent wire is flowing in the opposite direction, so we need to use a negative sign for I'. The formula becomes:

F = -(mu0*I*I')/(2*pi*d)

Again, we can simplify by plugging in the values for mu0 and d, and the current in the bottom wire, I. The direction of the force will be downward, opposite to the direction of the current in the bottom wire.

I hope this helps! Remember to always pay attention to the direction of the current and the distance between the wires when using the formula for magnetic force.