Magnetic force on a wire

Sheneron

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
[tex]F= ILB[/tex]

[tex]B = \frac{\mu_{0}I_{enc}}{2\pi r}[/tex]

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.
[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

ak1948

Do you mean .0064N/m

Sheneron

yes I did, sorry

Sheneron

I can't figure out what could be wrong with this.

naresh

Looks okay to me too..

Thomassino

The instructions request the direction as well as the magnitude...
You have the magnitude: 6.34mN/m
I'd say you need to articulate the direction ("inward"), ,otherwise you are absolutely correct.

Sheneron

Well I got an answer of 6.4mN/m which is not the right answer. 3 options. Something is wrong in my logic. Something is wrong in my calculations. Or the books is wrong.