Q. 15

# 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 A3 carrying current 1.5 I be placed between A1 and A2 so that it experiences no net force due to A1 and A2 ? Does the net force acting on A3 depend on the current flowing through it ?

Answer :

We know the force per unit length on two infinitely current-carrying wires if given by

Where I_{a} is current-carrying by wire A and I_{b }respectively

And d is the distance between parallel wires.

Force per unit length on wire A_{3} due to A_{1}

In –ve x-direction

And Force per unit length on wire A_{3} due to A_{2}

In +ive x direction

So for no net force on A_{3} both equation should be equal

at x = the net force on A_{3} will be zero.

Also, the net force acting on A_{3} depends upon the magnitude of the current flowing through it as we can conclude through the formula. However, its direction doesn’t affect our answer because one of A1 or A2 will cancel the effects produced by the wire A3.

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