# Force due to currents in parallel wires

1. Jul 9, 2008

### Knissp

The problem statement, all variables and given/known data

Two negative charges repel each other.
Two parallel wires with current going in the same direction attract each other.

Yet if one walks with the moving charge in the wires, the charges appear stationary and should repel each other - explain why if you are stationary with respect to the wire, they would attract while if you move with the charge they should repel."

The attempt at a solution
This is more of a conceptual question, so I really don't know how to approach it. Any help would be appreciated. I don't think the equations are relevant, but there's Coulomb's Law for static charges and the fact that currents going in the same direction in parallel wires attract, but I don't know how to resolve the issue of different frames of reference, i.e. the charges are stationary wrt the observer or the charges are moving wrt the observer and how this affects the force perceived.

2. Jul 9, 2008

### cryptoguy

Here's the gist: when you have stationary charges, the only force (apart from gravity) acting on them is the electrostatic force described by Coulomb's law. When you have a current, that force is still present, but there's a magnetic field around both the wires that causes the attractive force (according to the right-hand rule).

Now the magnetic force is stronger then the electrostatic force, as proven by the following equation between 2 parallel wires $$\frac{F}{l} = \frac{\mu_0 I_1 I_2}{2 \pi d}$$.
Note that F (magnetic force) decreases at a rate of 1/d (distance between wires) while in Coulomb's law, the electrostatic force decreases as a function of 1/d^2, which means that the magnetic force will be much stronger, causing the attraction.