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There is a long cylinder magnet is surrounded with a solenoid with same length and n=N/L turns per unit length carrying a current of . The magnet has radius of R, length of L and uniformly distributed total magnetic dipole of for r<R. (z: cylinder axis, constant, ∅: direction in cylindrical coordinates).
a.) Calculate magnetization M and bound currents (Clearly show your work and surfaces).
b.) Calculate the B, H everywhere. (Assume that the magnetic field of solenoid is not big enough to change magnetization of magnet)
c.) Calculate the magnetic vector potential everywhere.
d.) Calculate B again along z axis by assuming the L is short (L is not zero).
e.) Calculate the magnetic scalar potential of this magnet by assuming the cylindrical magnet is short and R is very large. (What is the electrostatic equivalent of this structure?
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