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EXAM1_Q_3

# EXAM1_Q_3 - The electric ﬂux density is 5:53[1—(1...

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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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