3. You have a magnetized cylinder of M = Mos with its axis along the z-axis, radius a and length L. Put the origin at the bottom of the cylinder. There is no free current. a. Find the bound volume and surface current densities. b. Write down the integral(s) for finding the vector potential A on the z-axis (Put the origin at the bottom of the cylinder): i. F = ii. F' iii. = iv. |2|= v. 2 = vi. dl', da', and/or dr' as appropriate for your integral(s). What are your limits of integration? vii. Write down the integral(s). You do not need to solve them. c. Given what you know about the direction of the bound currents, make a sketch showing an approximation of what B and H should look like inside and out. You do not need to solve for either one. Give a short descriptive explanation of your decisions, including any reasons B and H might be different from each other.

3. You have a magnetized cylinder of M = Mos with its axis along the z-axis, radius a and length L. Put the origin at the bottom of the cylinder. There is no free current. a. Find the bound volume and surface current densities. b. Write down the integral(s) for finding the vector potential A on the z-axis (Put the origin at the bottom of the cylinder): i. F = ii. F' iii. = iv. |2|= v. 2 = vi. dl', da', and/or dr' as appropriate for your integral(s). What are your limits of integration? vii. Write down the integral(s). You do not need to solve them. c. Given what you know about the direction of the bound currents, make a sketch showing an approximation of what B and H should look like inside and out. You do not need to solve for either one. Give a short descriptive explanation of your decisions, including any reasons B and H might be different from each other.