Distance separating current carrying wires.

[linuxux]

Homework Statement

How far from a wire with a current of 5.0A is a second parallel wire with current 10A if force between them is $$3.6x10^{-4} N$$?

Homework Equations

i think $$\frac{F}{L}=\left(\frac{u_o}{2\pi}\right)\left(\frac{I_{1}I_{2}}{s}\right)$$

The Attempt at a Solution

i think this just a simple plug and chug question, but is $$\frac{F}{L}$$ equal to $$3.6x10^{-4} N$$? what's the L for?

 

[chaoseverlasting]

F/L is force per unit length and yes, here F/l is 3.6x10^{-4}.

 

[m2003]

I would agree that this is a simple plug and chug question. The formula you provided is correct for calculating the force between two parallel current carrying wires, where F is the force, u_0 is the permeability of free space, I_1 and I_2 are the currents in the two wires, and s is the distance between the wires.

In this case, you are given the force (3.6x10^{-4} N), the current in one wire (5.0A), and the current in the other wire (10A). The only unknown variable is the distance between the wires, which is represented by L in the formula.

To solve for L, you would rearrange the formula to be L=\frac{u_o}{2\pi}\left(\frac{I_{1}I_{2}}{F}\right). Plugging in the given values, you would get L=\frac{(4\pi x 10^{-7})}{2\pi}\left(\frac{(5.0)(10)}{3.6x10^{-4}}\right)=0.00694 m.

Therefore, the distance between the wires is approximately 0.00694 meters. This calculation assumes that the wires are infinitely long and straight, and that they are parallel to each other.