Ampere's Law (Calculus) Practice Problems

A long cylindrical aluminum rod of radius 1 mm is surrounded by a copper cylindrical shell of inner radius R₁ and outer radius R₂. The two conductors are separated by an electrical insulator. The rod and the shell carry equal and opposite currents of magnitude I that are distributed uniformly across their volumes. Determine the magnitude of the magnetic field at point A located at a distance r > R₂ from the axis of the rod.

A tightly wound solenoid coil of length 85.0 cm and radius 3.0 cm has 2500 turns. You are asked to generate a magnetic field of 0.34 T at the center of the solenoid coil. What must be the current I in the turns to generate the necessary magnetic field?

Consider a closed loop that surrounds a long coaxial cable consisting of cylinder-shaped conductors spaced apart by an insulator. The anticlockwise line integral ∲B•dl around this loop is 1.27 × 10^-2 T•m. Determine the value of the clockwise line integral ∲B•dl.