Magnetic force on a wire

by Sheneron
Tags: force, magnetic, wire
 P: 360 1. The problem statement, all variables and given/known data 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? 2. Relevant equations $$F= ILB$$ $$B = \frac{\mu_{0}I_{enc}}{2\pi r}$$ 3. 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. $$\frac{\pi(0.002)^2}{\pi(0.005)^2}*100 = Number of Wires$$ That gives me 16 wires and since each has 2 amps the current enclosed = 32 A. Using ampere's law: $$B = \frac{(4\pi * 10^{-7})(32)}{2\pi(0.002)}$$ B = 0.0032 Knowning B I can find the force per unit length on one wire with 2 amps of current. $$\frac{F}{L} = (2)(0.0032)$$ 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