P32_013 - 13. An electric field with circular field lines...

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Unformatted text preview: 13. An electric field with circular field lines is induced as the magnetic field is turned on. Suppose the magnetic field increases linearly from zero to B in time t. According to Eq. 31-27, the magnitude of the electric field at the orbit is given by E= r 2 dB r = dt 2 B , t where r is the radius of the orbit. The induced electric field is tangent to the orbit and changes the speed of the electron, the change in speed being given by ∆v = at = eE t= me e me r 2 B t t= erB . 2m e The average current associated with the circulating electron is i = ev/2πr and the dipole moment is µ = Ai = π r2 ev 2πr = 1 evr . 2 The change in the dipole moment is ∆µ = 1 1 er ∆v = er 2 2 erB 2m e = e2 r 2 B . 4m e ...
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