A long straight cylindrical shell has an inner radius R_i and an outer radius R_o.It carries a current i, uniformly distributed over its cross section.A wire is parallel to the cylinder axis, in the hollow region (r R_o).We conclude that the wire: A)is on the cylinder axis and carries current i in the same direction as the current in the shell B)may be anywhere in the hollow region but must be carrying current i in the direction opposite to that of the current in the shell C)may be anywhere in the hollow region but must be carrying current i in the same direction as the current in the shell D)is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell E)does not carry any current

Question

A long straight cylindrical shell has an inner radius R_i and an outer radius R_o.It carries a current i, uniformly distributed over its cross section.A wire is parallel to the cylinder axis, in the hollow region (r < R_i).The magnetic field is zero everywhere outside the shell (r > R_o).We conclude that the wire: A)is on the cylinder axis and carries current i in the same direction as the current in the shell B)may be anywhere in the hollow region but must be carrying current i in the direction opposite to that of the current in the shell C)may be anywhere in the hollow region but must be carrying current i in the same direction as the current in the shell D)is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell E)does not carry any current

Quizplus · Accepted Answer

Since the magnetic field is zero outside the shell, we can conclude that the net magnetic field at any point inside the shell due to the current in the shell and the wire is zero. This means that the magnetic field due to the wire must be equal and opposite to the magnetic field due to the current in the shell. By applying the right hand rule, we can see that the current in the wire must be in the opposite direction to the current in the shell in order for the magnetic fields to cancel out. Thus, the wire must be on the cylinder axis and carry current i in the direction opposite to that of the current in the shell, which corresponds to choice D.

A Long Straight Cylindrical Shell Has an Inner Radius Ri

A Long Straight Cylindrical Shell Has an Inner Radius R_i