I learned in my undergraduate physics class that atoms have magnetic fields produced by the orbit of electrons and the spin of electrons. I understand how an orbit can induce a magnetic field because a charge moving in a circle is the same as a loop of current.
What I do not understand is how a spinning ball of charge can produce a magnetic field. Can someone explain how spin works, preferably in a way I can understand?
Answer
An electron is not a spinning ball of charge and the intrinsic spin of particles cannot be understood in such terms. Not only is it difficult to make sense of what it means for a pointlike particle to spin, but also when treating the electron as a spinning ball of charge one finds a value of the ratio between the magnetic moment and the angular momentum that is a factor $2$ too small.
To understand why a rotating charged ball generates a magnetic field, note that every charge on the ball will move in a circle, so there is in fact a current, and that current will generate a magnetic field.
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