Final answer:
A) The magnetic field inside the conductor is zero. B) The electric field inside the conductor is radially outward. C) The potential difference between any two points on the conductor is constant. D) The current density is inversely proportional to the radial distance from the z-axis.
Step-by-step explanation:
A) The magnetic field inside the conductor is zero because the magnetic field produced by the current in the conductor cancels out due to symmetry. The magnetic field lines form concentric circles around the conductor, but at any point inside the conductor, the magnetic field contributions from every point on the conductor cancel out.
B) The electric field inside the conductor is radially outward. According to Gauss's law for electric fields, the electric field inside a conductor is always perpendicular to the surface and points outward. Since the conductor has cylindrical symmetry, the electric field is radially outward.
C) The potential difference between any two points on the conductor is constant. This is because the electric field inside the conductor is zero (from part B), and the potential difference is directly proportional to the electric field. Therefore, the potential difference is constant throughout the conductor.
D) The current density is inversely proportional to the radial distance from the z-axis. The current density is defined as the current per unit area. Since the conductor is infinitely long and has cylindrical symmetry, the current is uniformly distributed in the z-direction. Therefore, the current density decreases as the radial distance from the z-axis increases.