Unformatted text preview: @ / The electric ﬂux density is 5:53 [1—(1+ Wch(—kR)]. I: R‘ a. Find the charge density p = V ' 5 h. DR appears to be inversely proportional to R2 as R A0, implying that:
a point charge is located at the origin. Show that this is untrue by nnding the 5
limit as R— O of DR Hint: Expand the exponential in its Taylor series;
er p LL = l + LL + LL12! + LL3/3l—i—  . Be sure to retain a sufﬁcient number of”
terms. The coaxial cylindricd capacitor of Fig
6 has a dielectric between its plates for
which the die lee 'tic constant varies as e“. = sop"
w ere ”0 a1; n are positive constmtts. ind the — f a length L of this system by
inning the energy in the nelds between the plates. Figure 6 plates. Capacitor with coaxial cyli Tind the amount of work required for“ rearranging a uniformly distributed sur—
I'E'face charge ,Q of radius a into a uniformly distributed volume charge of radius a. The region x > O is a perfect dielectric of permittivity 230 and the regionx < 0 is
a perfect dielectric of permittivity 380. Consider the ﬁeld components at point 1
on the +x side of the boundary to be denoted by subscript 1 and the ﬁeld com
ponents at the adjacent point 2 on the —x— s—ide of the boundary to be denoted by
subscript 2. If E1 = E0(2ax + 21,), ﬁnd the following. (a) E 1/ E 2; (b) El/Ez; and
(c) Dt/Dz Calculate the capacitance of two spheres of radius Rseparated by a large distance L >> {,3 ndrical ...
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 Spring '10
 Ferguson
 Electromagnet

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