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I have a test in a few hours, and my professor gave us a practice test, and I'm stuck. Could you give me a hint as to how to approach this problem, equations I could use. It's an algebra based class so I'd avoid using calculus equations. Thank you.

Three thin infinite wires carrying currents I in the same direction go perpendicularly to the paper sheet that they intersect at the points forming an equilateral triangle of side L. Calculate the force acting on each wire per unit length. What is the direction of the forces?

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    $\begingroup$ What equations have you learned in class about forces on current-carrying wires? $\endgroup$ – Flavin Nov 5 '13 at 20:05
  • $\begingroup$ The one I thought of using is F = (1/4PiE0)(q1q2/r^2) But I'm not sure how to get the charges, and I assume r would be L? $\endgroup$ – aNxello Nov 5 '13 at 20:15
  • $\begingroup$ That looks like an equation for the force on a point charge due to another point charge. I bet you have learned some equation about forces on wires. $\endgroup$ – Flavin Nov 5 '13 at 20:25
  • $\begingroup$ $ \frac{F}{\Delta L} = \frac{\mu_0 I_1 I_2}{2\pi r} $ $\endgroup$ – aNxello Nov 5 '13 at 20:50
  • $\begingroup$ What would u0 and r be though? Wouldn't it be just L, since that's the radius of the magnetic field? $\endgroup$ – aNxello Nov 5 '13 at 20:50
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You essentially answered your own question in your comment.

The force per unit length between two current-carrying wires is $$\frac{F}{\Delta L} = \frac{\mu_0 I_1 I_2}{2 \pi r}$$ For a derivation, see here.

The currents are all equal, $I_1=I_2=I_3=I$. The distances are all equal, $r_{12}=r_{13}=r_{23}=L$. $\mu_0 =4\pi \times10^7 N/A^2$ is a constant, so you can leave it in your answer as $\mu_0$.

This will only give you the magnitude of the force. You will need to figure out the direction from the directions of the magnetic fields.

To get the force $F_1$ on wire 1, you can consider the force $F_{12}$ on wire 1 from wire 2, then add the force $F_{13}$ on wire 1 from wire 3. (Remember to add the forces as vectors! Their directions will matter.) Once you find the force on wire 1 (including direction), the forces on wire 2 and wire 3 will have the same magnitude, and you should be able to find their directions easily.

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    $\begingroup$ Thank you! I'm sorry I wasn't so clear at the time of posting my question, I'll try to improve in the future. $\endgroup$ – aNxello Nov 5 '13 at 21:17

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