# Two infinitely long straight wires A1 and A2 carrying currents I and 2I flowing in the same directions are kept ‘d’ distance apart. Where should a third straight wire carrying current 1.5 I be placed between  and  so that it experiences no net force due to and   ? Does the net force acting on   depend on the current flowing through it ?

As we know the force per unit length on two infinitely current-carrying wires is given by Where is current carrying by wire A  and by wire and d is the distance between parallel wires.

Now, force per unit length on wire due to

In -ve x-direction.

and force per unit length on wire due to .

In +ve x- direction.

So, for net force on , both the equations should be equal.

therefore,

if  the net force on will be zero.

Net force depends on the current flowing.

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