Question

Show that two parallel currents attract each other. Show your work.

Answer 1

Two parallel current attract each as force exerted by each current carrying wire is directed towards each other

One current carrying will have a magnetic field at the location of other current carrying wire.

So each current carrying wire lies in magnetic field created by other wire. And force is experienced by current carrying wire in magnetic field.

F F, B1 B2

Current in both wires is in same direction but magnetic field created by wire 1 on left is into the page at location of right wire

Similarly direction of magnetic field due wire 2 on right is out of page at location of left wire.

Direction of force is obtained using right hand rule at each wire

As $\vec F = I \vec l \times \vec B$

Force on left wire is towards right

and on right wire , force is towards left

so both wires attract each other.

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