1. A long copper wire of cross-sectional radius R carries a uniform current I. What is the current density j(r)? Use Ampere's Law to determine B as a function of the distance a from the centre of the wire. Sketch the result.
2. A long copper pipe with thick walls has an inner radius R and an outer radius 2R. A current I flows along this wall, uniformly distributed over the cross-sectional area of the copper. What is the current density j(r) for all r? Use Ampere's Law to find the magnetic fields as a function of radial distance from the centre of the pipe. Sketch the result.
3. A coaxial cable consists of a long cylindrical copper wire of radius r₁ surrounded by a cylindrical insulating shell of outer radius r₂. A final conducting cylindrical shell of outer radius r₃ surrounds the insulating shell. The wire and conducting shell carry equal but opposite currents I uniformly distributed over their volumes. What is the current density j(r) for all r? Find formulas for the magnetic field in each of the regions 0 < a < r₁, r₁ < a < r₂, r₂ < a < r₃, and a > r₃. Sketch the result.
4. A long copper wire of cross-sectional radius R carries a current density j(r) = Ae^-Kr. Use Ampere's Law to determine B as a function of the distance a from the centre of the wire. Sketch the result. The integral identity may be of use.
5. For the following magnetic fields, determine the current density J.
1. B_x = 2xy, B_y = 2z+3, and B_z = 5–2yz.
2. B_x = y³–z³, B_y = z³–x³, and B_z = x³–y³ .

6. For the magnetic fields in question 6, determine the current I inside the rectangle with the vertices (4,5,2), (8,5,2), (8,10,2), and (4,10,2). Integrate around the rectangle in the order of the given vertices.
7. A magnetic dipole is given by m = 4i + 7j - 4k. Determine the force on this dipole if it is placed in each of the possible magnetic fields in question 5.
8. In the Bohr model of the hydrogen atom, an electron in the ground state has a speed of 2.20 ´ 10⁶ m/s at a radius of 5.29 ´ 10^-11 m. The charge of an electron is 1.60 ´ 10^-19 C. Find the magnetic dipole moment of the atom.

Questions?mike.coombes@kwantlen.ca