# Magnetc force from current-carrying wires - help

1. Oct 20, 2004

### vsage

In the figure below, a long straight wire carries a current of 8.5 Amps.
(Attached)
Find the magnitude of the net force (in N) on a rigid square loop of wire of side, L, equal to 5.35 cm. The center of the loop is d = 10.40 cm from the wire and the loop carries a current of 10.0 Amperes.

I don't really know where to start on this one. I realize that the segments perpendicular to the length of wire with current I1 can be discarded as not contributing any force right? I don't know where to proceed from there. Your help is greatly appreciated.

Well I sort of figured out how to do it but I think I'm screwing the sign up somewhere:

$$F = iL \cross B$$
$$B = \frac{\mu I_1}{2 \pi r}$$
And sum up the force on the top and bottom of the square from the long wire? Do I add the force being exerted on the top of the loop from the bottom of the loop and vice versa?

Edit: Here is my work (let subscript t be top and b be bottom)

$$F = \frac {u_0I_1I_t L_t}{2 \pi r_t} + \frac {u_0I_1I_bL_b}{2 \pi r_b}$$

$$F = \frac {2 \times 10^{-7} \times 8.5 \times -10 \times 0.0535}{0.07725} + \frac {2 \times 10^{-7} \times 8.5 \times 10 \times 0.0535}{0.13075} = about 9 \times 10^-6N$$

which is wrong

#### Attached Files:

• ###### prob4.bmp
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Last edited by a moderator: Oct 20, 2004
2. Oct 20, 2004

### vsage

Nevermind I got it. I have been plugging in the wrong numbers for hours :\