In a classical current loop, tex2html_wrap160 tex2html_wrap161 torque.

Work required to go from tex2html_wrap162 to tex2html_wrap163 is tex2html_wrap164

classically tex2html_wrap165


tex2html_wrap166 where g is a proportionality constant (=1 for L).

tex2html_wrap167 tex2html_wrap168

tex2html_wrap169 =bohr magneton = tex2html_wrap170

classical electron radius is tex2html_wrap171

g=2 from stern gerlach experiment. Actually, tex2html_wrap172 . This can be calculated to almost the same accuracy, and it agrees.

QM derivation:

Hamiltoian in external classical uniform B field:


since tex2html_wrap174 , this is tex2html_wrap175

= tex2html_wrap176

tex2html_wrap177 where tex2html_wrap178 .

Ratio between 2nd and 3rd terms is tex2html_wrap179

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