Answer Happy

1 A Strange Dipole Consider the distribution of charges pictured below. In this problem we will calculate the electric field of this distribution on the positive z-axis and approximate its behavior far from the origin. ward 1 (a) Calculate [10pts] Use superposition to find an exact expression for the electric field at an arbitrary point on the z-axis with > E (b) Simplify [5pts] Pull out a factor from your expression from (a). Your answer should now look like: = 5/2 kq There should be three terms in the parenthesis.

(c) Approximate [10pts] We will now approximate our answer in the limit that z >> or equivalently<< 1. Consider the binomial approximation, that for r << 1: 1 (1 -mx) (1+x)n Apply this approximation to your answer from (b) and simplify. (d) Unit Check [5pts] Make sense of your answer by checking that the units are correct. (e) Dipole Moment [5pts] In class we found that the electric field (on the z-axis) of a dipole has the form: Ε = 2kp 23 What would you need to plug in for the dipole moment, p, to get this to match your answer from (c)? (f) Dipole Calculation [5pts] In general, the dipole moment of a distribution of point charges can be calculated as: P = ΣQiri Calculate the dipole moment of this charge distribution and make sure it matches your answer from (e).