magnetic forces on two current carrying wires

endeavor

"Find the force per unit length on each of two long, straight, parallel wires that are 24 cm apart when one carries a current of 2.0 A and the other a current of 4.0 A in the same direction."

Tell me if I'm doing this right:
I use d = 0.24m, and the equations B = (mag. perm. * I)/(2*pi*d), and F = ILB.

The force per unit length on each wire is then: F/L = IB.

Plugging in I and B for each of the wires, I get:
F/L (for the 2.0A wire) = 3.3 * 10^-6 N/m (toward the other wire)
F/L (for the 4.0A wire) = 1.3 * 10^-5 N/m (toward the other wire)

I think it's wrong because the answer is supposedly: "6.7 * 10^-6 N/m; attractive". But I would think that the forces are different on each wire, because the wires are carrying different currents...

arunbg

Your formulae are correct, however I can't see how you obtained your two different answers.
Remember, the expression you wrote explicitly is
[tex]\frac{\mu_0I_1I_2}{2\pi d}[/tex]

Can you possibly have two different answers ? :)

endeavor

oh ooops.
I did (F/L)₁ = I₁B₁, not I₁B₂!

arunbg

Thought so