Question

Suppose two long straight wires run perpendicular to one another without touching. Does one exert a net force on the other? If so, what is its direction? Does one exert a net torque on the other? If so, what is its direction? Justify your responses by using the right hand rules.

a) Yes, both wires exert an attractive force on each other; no torque is exerted.

b) Yes, both wires exert a repulsive force on each other; torque is exerted in the direction perpendicular to the wires.

c) No, the wires do not exert any force or torque on each other.

d) Yes, both wires exert a repulsive force on each other; no torque is exerted.

Answer 1

Two long straight wires running perpendicular to each other do not exert a net force or net torque on each other, because the magnetic field lines at the location of each wire are parallel to that wire, resulting in zero net force and torque according to the right hand rules.

Step-by-step explanation:

When two long straight wires are positioned perpendicular to each other without touching, the magnetic fields they create at the location of the other wire will be straight lines that run parallel to the other wire. According to the right hand rules for magnetism, a wire carrying a current creates a magnetic field that circles the wire. The direction of the field lines depends on the direction of the current, and this can be determined using the right hand rule (RHR-2).

If the currents in the two wires are flowing, then a magnetic force will exist between them. However, since the wires are perpendicular and not parallel, the direction of the magnetic field produced by one wire at the location of the second wire is parallel to the second wire. It cannot push or pull on the wire into which it is running parallel. Therefore, one wire does not exert a net force on the other. Similarly, there is no lever arm to generate a torque because the force is zero; hence, no net torque is exerted either.