# The Force Between Current-Carrying Conductors

#### vrobins1

1. Homework Statement

Consider two straight conductors of length 1 m, each of them carrying a current of I = 2 A. If they are placed 1 m apart, what is the magnitude and direction of the force between these two conductors if there currents are
a) in the same direction;
b) in the opposite direction.

2. Homework Equations

I know that

B = $$\mu$$0*I/2$$\pi$$r

I also know that that force on a conductor in general is F = ILBsin$$\theta$$.

3. The Attempt at a Solution

I calculated the magnitude of B according to the equation above and got 3.95-5 T.

I'm not sure how to find the force of TWO conductors together though.

Would you just do F = ILB for both conductors, adding the two F values of they are going in the same direction and subtracting if they are going in opposite directions?

Is the direction determined by the RHR?

Any insight would be much appreciated. Thanks!

Last edited:
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#### Doc Al

Mentor
I'm not sure how to find the force of TWO conductors together though.

Would you just do F = ILB for both conductors, adding the two F values of they are going in the same direction and subtracting if they are going in opposite directions?
Not exactly. To find the force on wire #2, start by finding the field from wire #1, then find the force it exerts on wire #2. That's it: the force that wire #1 exerts on wire #2. Of course, wire #2 exerts the same force on wire #1. (Don't add/subtract the F values.)
Is the direction determined by the RHR?
Yes. The direction of the field created is determined by the RHR, and so is the direction of the force that each wire exerts on the other.

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