Problem 23.

Problem 23.68 A thin rod of length 2l has a linear charge density that is lembda o at the left end but decreases linearly with distance going from left to right in such a way that the charge on the entire rod is zero.

Part A What is the magnitude of the electric field along the rod?s axis at a position P that is a distance d>l to the right of the center of the rod? Use the notation l for the variable l. Express your answer in terms of the variables l, lembda o, d, and Coulomb's constant k.

Part B How does your expression simplify to a familiar result for the limiting case d>>l? (hint: The dipole moment of the rod has magnitude p = 2 lembda ol^2/3.) Express your answer in terms of some or all of the variables p,d, and Coulomb?s constant k.