Force on a long straight wire help

Lost4468

I'm not sure about the force 3 wires have, here's the question.



The question is:

"Calculate the force per unit length experienced by the middle wire in the arrangement shown."

The thing is I've an overall force of 0 because I1 and I3 are in different directions each producing a force of 0.15Nm^-1. Surely that's wrong? I think the middle wire somehow has an effect but I don't know how.

I like Serena

Lost, welcome to PF!

If 2 wires have currents in the same direction, they repel each other (with an equal but opposite force).
If 2 wires have currents in opposite directions, they attract each other.

So they do not cancel - they amplify each other (on the wire in the middle).

However, I get a different value for the force than what you have.
How did you calculate it?
Which formula did you use?

Lost4468

Nevermind I had the calculation wrong, I found an old mark scheme for it and it says that there's no overall force on the middle wire. Thanks.

I like Serena

Weird, since I believe there is an overall force on the middle wire.

davenn

they ( any induced currents from the 2 outer wires) would only cancel in the middle wire if there was no initial current flowing in the middle wire.

I have to assume from the diagram that the 2A flowing in the middle wire is a pre-existing current, so as you say there would be an overall force in the middle wire

cuz the induced current flow from external sources would cancel cuz they are equal and opposite and leave just the initial 2A flowing in the middle wire?

does that sound right ?

Dave