A long cylindrical wire has radius R and carries current I. In this problem, we'll find the energy stored in the magnetic field inside the wire. (a) Find the magnetic field inside the wire, as a function of the distance r from the center of the wire. You can assume that the current is distributed uniformly over its cross-sectional area. Hint: This is similar to part (a) of the Canvas portion of Homework 8. (b) Write an expression for the energy density of the magnetic field inside the wire, again as a function of the distance r from the center of the wire. Note that energy is not the same as energy density. You should check that your answer has units of J/m3 before moving on to the next part. (c) Integrate your energy density over the cross-sectional area of the wire to get the energy per unit length stored in the magnetic field inside the wire. (Don't worry about the field outside the wire, which also stores energy.) Your final answer should have units of J/m.

A long cylindrical wire has radius R and carries current I. In this problem, we'll find the energy stored in the magnetic field inside the wire. (a) Find the magnetic field inside the wire, as a function of the distance r from the center of the wire. You can assume that the current is distributed uniformly over its cross-sectional area. Hint: This is similar to part (a) of the Canvas portion of Homework 8. (b) Write an expression for the energy density of the magnetic field inside the wire, again as a function of the distance r from the center of the wire. Note that energy is not the same as energy density. You should check that your answer has units of J/m3 before moving on to the next part. (c) Integrate your energy density over the cross-sectional area of the wire to get the energy per unit length stored in the magnetic field inside the wire. (Don't worry about the field outside the wire, which also stores energy.) Your final answer should have units of J/m.