P25_034 - 34. (a) Consider an infinitesimal segment of the...

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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.

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