# Mutual force between AC current carrying wires

1. Sep 28, 2015

### fog37

Hello Everyone,

Two wires carrying DC currents directed in the same direction attract each other (repel if the currents go in opposite directions).

What happens if the currents in the two wires are AC instead of DC? I think it depends on the frequency and length of the wire. Some sections of the wires will attract while other sections will repel. The final effect will be determined by the net force from the various pairs of segments.

What do you think?

thanks!

2. Sep 28, 2015

### fog37

Thanks.

Ok, that assume that each segment on one of the wires faces a segment on the other wire two having current going in the opposite direction. So overall there would be a repulsion between the two wires. That is if the two wires have equal length and the currents are 180 out of phase.

but if the currents relative phase is not 180, I guess the net force could be attractive...

3. Sep 28, 2015

### andrewkirk

Based on the rule you've given, the two wires will be attracted everywhere except for a nil force in some spots if the currents are in phase, and will be repelled everywhere except for a nil force in some spots if the currents are 180 degrees out of phase. For any other phase difference, they will attract in some places and repel in others - eg consider the sin and cos functions, which are sometimes both the same sign and sometimes different. I expect the net force will be attraction if the phase diff is less than 90, otherwise repulsive.

Where does this force come from though? I can't see how it would arise from Maxwell's equations. Is it a quantum thing, or am I missing something obvious in Maxwell?

4. Sep 28, 2015

### Staff: Mentor

It comes from the Lorentz force acting on the moving electrons in the wires. The moving electrons in one wire generate a circulating B-field around that wire that causes the Lorentz force on the moving electrons in the other wire, and visa-versa...

5. Sep 28, 2015

### meBigGuy

6. Sep 29, 2015

### Baluncore

Consider a return circuit of two wires separated by distance, d, with equal and opposite DC current in the two wires.
Now if one wire is fixed it will generate a B field proportional to the current in the region of the return wire.
The repulsive force per unit length on the return wire will be F = μ0 * I2 / ( 2 * π * d)