Cylindrical Permanant Magnet Viewed as a Solenoid In this we view the sum of all the atomic dipole moments in a given cross section of the cylinder as a single current loop of radius equal to that of the cylinder and current equal to qw where q is the electron charge and w is its rotation rate in radians per second. The magnetic field at macroscopic distance r from the cylinder is described by the Biot-Savart law as: B=Sumi(integral(i(dlxr)/r^3)) over all the atomic orbitals in the cross section or, what amounts to the same value, it is B=integral(i(dlxr)) where the integral is around the circumference of the cylinder. The important thing to note is that most of the current due to the orbitals cancel out and we are left with large rings of current in the clockwise direction. In fact it is shown that the total magnetic moment of the uncancelled large current rings is the same as the sum of the moments of the electron orbitals. Therefore, it is a good approximation to view the permanent magnet as a cylindrical solenoid.
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