Consider a magnetic dipole carrying a current I.
a. Calculate the magnetic flux density B(vector) at a point P specified in spherical coordinates. Express the answer in terms of the magnetic dipole moment m(vector) . For full credit, fill all the details and justify all the assumptions adopted.
b. Sketch the magnetic flux density B(vector) and compare the results with the results for E(vector) in an electric dipole. Discuss.
c. Please address the following questions.
i. Describe the importance of the magnetic vector potential A(vector) in the calculations above.
ii. Can you give other examples of the usefulness of A(vector) ?
iii. What is the magnetic scalar potential Vm ? How is it different than A(vector) ?