A more challenging example for self-study Q4. We introduce a second conductor whose cylindrical axis is located at x D with identical dimensions as the first. Assume that charge-Q is uniformly distributed on the surface of the second conductor. a) Express the electric field on the x-axis anywhere between the two conductors (y = 0,a

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A more challenging example for self-study
Q4. We introduce a second conductor whose cylindrical axis is located at x D with identical dimensions as
the first. Assume that charge-Q is uniformly distributed on the surface of the second conductor.
a) Express the electric field on the x-axis anywhere between the two conductors (y = 0,a<x<D-a)
E=&-
PL
Σπερχ
Pi
+8
2πЕo (D-x)
+Q
a
a
D
b) Using the result of a), express the voltage difference between the surfaces of the two conductors, V12-
V12
=-
a
D-a
PL
2πο
a
Pi
(dx
E-dx=
2περ
x
D-a
x = a
Inxx =D-a
Pu
-a
=
περ
a
Transcribed Image Text:A more challenging example for self-study Q4. We introduce a second conductor whose cylindrical axis is located at x D with identical dimensions as the first. Assume that charge-Q is uniformly distributed on the surface of the second conductor. a) Express the electric field on the x-axis anywhere between the two conductors (y = 0,a<x<D-a) E=&- PL Σπερχ Pi +8 2πЕo (D-x) +Q a a D b) Using the result of a), express the voltage difference between the surfaces of the two conductors, V12- V12 =- a D-a PL 2πο a Pi (dx E-dx= 2περ x D-a x = a Inxx =D-a Pu -a = περ a
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