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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. 3127, 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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 Fall '08
 SPRUNGER
 Physics

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