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 Ia is current-carrying by wire A and Irespectively


And d is the distance between parallel wires.


Force per unit length on wire A3 due to A1


In –ve x-direction


And Force per unit length on wire A3 due to A2


In +ive x direction


So for no net force on A3 both equation should be equal





at x = the net force on A3 will be zero.


Also, the net force acting on A3 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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