Our text claims that a charged particle exerts a net attractive force on an electric dipole. The purpose of this exercise is to investigate this phenomenon. Suppose a permanent dipole is situated at the origin of the r-z plane and consists of charges +q and -9 separated by a fixed distance s. The dipole is situated such that +q lies at -- on the r-axis and -q lies at on the r-axis. A charge +Q is situated at distance r from the center of the dipole on the positive r- axis. We'll assume, as is usually the case for electric dipoles, that s
a. (1 point) Draw a pictorial representation of this physical situation and label any quantities of interest.

b. (2 points) Write an expression for the net force exerted on the dipole by charge +Q.

c. (1 point) Is this force toward + or away from +Q? Explain.

d. (3 points) Use the binomial expansion as an approximation tool to understand the effect that s«r has on the physical situation. The binomial approximation to first order is written: (1 + x)" ~1 - nx if x« 1

Using the binomial approximation, simplify your expression from part (a) for the net force exerted on the dipole from charge +Q. Asses the validity of your solution by analyzing the physical units to make sure that your solution has units of force.

e. (1 point) How can the electric force have an inverse-cube dependence? Doesn't Coulomb's law assert that the electric force depends on the inverse square of distance? Explain.

f.(2 points) What happens to the value of the force in the limit as s → 0. What does s → 0 mean physically?