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Unformatted text preview: 34. (a) Consider an inﬁnitesimal segment of the rod from x to x + dx. Its contribution to the potential at
point P2 is
1
1
λ(x)dx
cx
=
dx .
dV =
4πε0 x2 + y 2
4πε0 x2 + y 2
Thus,
V= dVP =
rod c
4πε0 L
0 x
x2 + y 2 dx = c
( L2 + y 2 − y ) .
4πε0 (b) The y component of the ﬁeld there is
Ey = − ∂VP
cd
=−
(
∂y
4πε0 dy L2 + y 2 − y ) = c
4πε0 1− y
L2 + y2 . (c) We obtained above the value of the potential at any point P strictly on the y axis. In order to obtain
Ex (x, y ) we need to ﬁrst calculate V (x, y ). That is, we must ﬁnd the potential for an arbitrary point
located at (x, y ). Then Ex (x, y ) can be obtained from Ex (x, y ) = −∂V (x, y )/∂x. ...
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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