Magnetic Force Per Unit Length

[Ithryndil]

Homework Statement

A packed bundle of 100 long, straight, insulated wires forms a cylinder of radius R = 0.600 cm.

If each wire carries 4.50 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?

Homework Equations

$$F/L = IB$$
$$B = (\frac{(\mu)I}{2(\pi)R^{2}})r$$

The Attempt at a Solution

I plugged in the various values getting:

$$F/L = (450)((4\pi X 10^{-7}*450)/(2\pi(.006^{2}))(.002)$$

That equals 2.25 N/m which is orders of magnitude off. Can anyone tell me what I am doing wrong here? This problem is in the book with slightly different numbers and the answer is is X.XX mN/m. Thanks for the help.

 

[Ithryndil]

Anyone know where I am going wrong?

 

[alphysicist]

Hi Ithryndil,

Homework Statement

A packed bundle of 100 long, straight, insulated wires forms a cylinder of radius R = 0.600 cm.

If each wire carries 4.50 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?

Homework Equations

$$F/L = IB$$
$$B = (\frac{(\mu)I}{2(\pi)R^{2}})r$$

The Attempt at a Solution

I plugged in the various values getting:

$$F/L = (450)((4\pi X 10^{-7}*450)/(2\pi(.006^{2}))(.002)$$

I don't think this is correct. The B-field part looks right to me, but if you then compare this to your first equation F/L = IB, this would be the force per unit length on a single wire that has a current of 450A.