Ampere's law: A very long, solid, conducting cylinder of radius R carries a current along its length uniformly distributed throughout the cylinder. Which one of the graphs shown in the figure most accurately describes the magnitude B of the magnetic field produced by this current as a function of the distance r from the central axis?

Question

Quizplus · Accepted Answer

Ampere's law tells us that the magnetic field around a long, straight current-carrying wire is proportional to the current divided by the distance from the wire. In this case, since the current is uniformly distributed throughout the cylinder, we can assume that it is equivalent to a wire of the same length carrying the same current. Therefore, the magnetic field will depend on the distance from the central axis, and not on the distance from the cylinder's surface.

Option A best represents this relationship, as the magnetic field is constant for any points within the radius of the cylinder, and decreases proportional to the inverse of the distance for points outside the cylinder. Options B through E do not accurately represent this relationship, as the magnetic field is shown to increase or decrease as the distance from the surface increases, which is not true for a long, solid, uniformly current-carrying cylinder.

Ampere's Law: a Very Long, Solid, Conducting Cylinder of Radius