Magnetic Field around a Bundle of Wires

[martellaj]

Homework Statement

A packed bundle of 100 long, straight, insulated wires forms a cylinder of radius R = 0.800 cm. If each wire carries 1.50 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. The attempt at a solution
My friend and I have been going over this problem for a while - this is what we have come up with so far:

Without a picture, we have decided the bundle is like a pull and peel Twizzler, just a bundle of 100 straight wires. The radius that we're attempting to find the force per unit length is .200 cm away, which is obviously smaller than the radius of the entire bundle so we're using:

B = (mu_0 * I * r) / (2 * pi * R^2)

- B is the magnetic field
- mu_0 is 4*pi*e-7
- I is 1.5 A
- r is .002 m
- R is .008 m

The answer we got was something like 9.375e-4, which is apparently within 10% to 100% of the actual answer, so the answer will be in the e-4 magnitude.

Any help would be great, and sorry I couldn't write the equation all fancy-like. Cheers.

 

[martellaj]

And I forgot to mention that we did in fact multiply the equation used by 100 to take in account of all 100 wires.

 

[martellaj]

Can anyone solve this in 3 minutes? It'd be great.