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Sheneron
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Homework Statement
A packed bundle of 100 long, straight, insulated wires forms a cylinder of radius R = 0.500 cm.
(a) If each wire carries 2.00 A, what are the magnitude and direction of the magnetic force per unit length acting on a wire located 0.200 cm from the center of the bundle?
Homework Equations
[tex]F= ILB[/tex]
[tex]B = \frac{\mu_{0}I_{enc}}{2\pi r}[/tex]
The Attempt at a Solution
Here is what I did to get the solution:
I can find the number of wires in out to where the radius equals 0.002m.
[tex]\frac{\pi(0.002)^2}{\pi(0.005)^2}*100 = Number of Wires[/tex]
That gives me 16 wires and since each has 2 amps the current enclosed = 32 A.
Using ampere's law:
[tex]B = \frac{(4\pi * 10^{-7})(32)}{2\pi(0.002)}[/tex]
B = 0.0032
Knowning B I can find the force per unit length on one wire with 2 amps of current.
[tex]\frac{F}{L} = (2)(0.0032)[/tex]
That equals 0.0064 N/m
That answer is wrong and I can't figure out why. If anyone can help it would be appreciated. Thanks
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