Question

A long, cylindrical conductor is solid throughout and has a radius 2.9cm. Electric charges flow parallel to the axis of the cylinder and pass uniformly through the entire cross section. The arrangement is, in effect, a solid tube of current 2.0A. Use Ampère's law to find the magnetic field inside the conductor at a distance 2.2cm from the axis. (Hint: For a closed path, use a circle of radius r perpendicular to and centered on the axis. Note that the current through any surface is the area of the surface times the current density.)

Answer 1

To find the magnetic field inside the conductor at a distance 2.2cm from the axis, we can use Ampère's law and consider a circular path perpendicular to and centered on the axis of the cylinder. The current enclosed by this path is the product of the current density and the area of the circle.

Step-by-step explanation:

To find the magnetic field inside the conductor at a distance 2.2cm from the axis, we can use Ampère's law. Ampère's law states that the integral of the magnetic field along a closed path is equal to the product of the permeability of free space (μ0) and the current enclosed by the path. We can consider a circular path of radius 2.2cm perpendicular to and centered on the axis of the cylinder. The current enclosed by this path is the product of the current density and the area of the circle. The current density is given as the total current (2.0A) divided by the cross-sectional area of the cylinder. Using these values, we can calculate the magnetic field inside the conductor at a distance 2.2cm from the axis using Ampère's law.