Question

Two very long current–carrying wires are shown end on in the figure. The wire on the left has a 4A current going into the plane of the paper and the wire on the right has a 3A current coming out of the paper. Disregarding the case of x → ∞, in which region(s) could the magnetic field from these two wires add to zero on the x–axis.

A) Region I only 

B) Region II only 

C) Region III only 

D) Regions I and III only 

E) none

Answer 1

The correct option is: (C) Region III only 

Explanation:

First of all we should state that a larger current makes a bigger B field and the further from the wire the less the B field. Using RHRcurl, the 4A wire has decreasing magnitude B fields pointing down in regions II and III on the axis and upwards on region I. The 3A wire has B fields pointing upwards in region III and downwards in regions II and I. To cancel, fields would have to oppose each other. Region I is a possibility but since the distance from the 4A wire is smaller at every point and it also has a larger current it will always have a larger B field so there is no way to cancel. Region II has fields in the same direction and cannot cancel. Region III has opposing fields. Since the 4A wire has a larger current but also a larger distance away from any point in Region III and the 3A wire has a smaller current but a closer distance to any point in Region III it is possible that these two factors compensate to make equal B fields that oppose and could cancel out.