Question

A square loop of current-carrying wire with edge length a is in the xy plane, the origin being

at its center. Along which of the following lines can a charge move without experiencing a
magnetic force?
A. x = 0, y = a/2
B. x = a/2, y = a/2
C. x = a/2, y = 0
D. x = 0, y = 0
E. x = 0, z = 0

Answer 1

A charge moving along the line x = 0, z = 0 (option E) would be moving parallel to the magnetic field lines produced by the current-carrying square loop and would not experience a magnetic force.

Step-by-step explanation:

The question deals with the motion of a charge in the magnetic field produced by a current-carrying square loop. According to the right-hand rule, the magnetic field lines will be coming out of the page (in the +z direction) within the square loop and going into the page (in the -z direction) outside the loop in the xy-plane because the current is in the loop's plane.

A charge moving parallel to a magnetic field experiences no magnetic force. Therefore, to find where a charge can move without experiencing a magnetic force, we need to locate where it would move parallel to the magnetic field lines produced by the loop. Along the line x = 0, z = 0 (option E), a charge would be moving directly along the wire in the xy-plane, and thus parallel to the magnetic field lines, since they point in the +z or -z direction within the plane of the loop. Thus, it wouldn't experience any magnetic force.