77. A small section of the distribution that has charge dq is λ dx, where λ = 9.0 × 10–9 C/m. Its contribution to the field at xP = 4.0 m is G dE =
dq
b
4 πε 0 x − x P
g
2
pointing in the +x direction. Thus, we have G 3.0 m E=³ 0
λ dx 4πε 0 ( x − xP )
2
ˆi
which becomes, using the substitution u = x – xP, G E=
λ 4 πε 0
z
−1.0 m
− 4 .0 m
FG H
IJ K
λ −1 −1 du i= − i 2 . m −4.0 m 4 πε 0 −10 u
which yields 61 N/C in the +x direction.