Consider a little electric dipole (like e. g., a polar molecule) with a charge +q (q > 0) located at
x = −d and another charge −q which is located at x = d.

a) [10 pts] determine the electric field e for points along the y-axis. briefly discuss how the
direction of your result for e makes sense.
b) [12 pts] for your solution in part a) consider the limit |y| » d, i. e. a point along the
y-axis very far away:
• define e as a function of y and d, such that e is a small quantity and expand your
solution in a power series up to fourth order in e.
• show that the units of your power series’ answer are correct.
• for what values of y does your expansion converge?
• why doesn’t your solution behave like coulomb’s law, i. e., why isn’t |e| ∝ 1/y2
here?