Unformatted text preview: PHY 5346
HW Set 1 Solutions , Kimel 2. 1.10 I will base the solution on the application of Green’s theorem, which results in eq. 1.36 from the textbook: 1 (w) 1 1 EMS 8 1
—¢ 10 $ 3 I I
= — d — — — — — — d
¢(x) 471—80 V R :17 + 471' S : <R): a
Since the volume includes no charge, the ﬁrst term on the rhs vanishes. For the second term 8gb —» A ’ A
WZV¢'TL/=—E‘nl
Note
% E  ﬁ’da’ = / 6/  EdP’x’ by the divergence theorem
S V
Using the fact that v4]? = pea/so then the second term of the ﬁrst equation also vanishes, since the volume integrated over contains no charge.
% (i) = — #, Where R is the radius of the sphere, and I’m taking the origin at the center of the sphere, 1
Mg) 2 47rR2 f ¢(f’)da’ = mean value of the potential over the sphere.
S Since ...
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 Spring '08
 smith

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