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Unformatted text preview: 29. Consider an inﬁnitesimal segment of the rod, located between x and x + dx. It has length dx and contains charge dq = λ dx = cx dx. Its distance from P1 is d + x and the potential it creates at P1 is dV = 1 1 cx dx dq = . 4πε0 d + x 4πε0 d + x To ﬁnd the total potential at P1 , integrate over the rod: V= c 4πε0
L 0 c x dx [x − d ln(x + d)] = d+x 4πε0 L =
0 L c L − d ln 1 + 4πε0 d . ...
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