My question is regarding the electric field of a dipole.

In the course notes for "Electric Fields and Continuous Charge Distributions", it concludes that the field in the x direction is (3pK / r^3) sin(theta) cos(theta)... and similar for the y direction. I can't figure out how to reach this conclusion. I know the dipole field is supposed to drop off as r^3, but since sin(theta) = x/r and cos(theta) = y/r, this would mean it drops off as x^5 !!!

Question

My question is regarding the electric field of a dipole. 

In the course notes for "Electric Fields and Continuous Charge Distributions", it concludes that the field in the x direction is (3pK / r^3) sin(theta) cos(theta)... and similar for the y direction. I can't figure out how to reach this conclusion. I know the dipole field is supposed to drop off as r^3, but since sin(theta) = x/r and cos(theta) = y/r, this would mean it drops off as x^5 !!!

anonymous · Answer

Watch the problem solving help video called "An Electric Dipole". It is here: http://ocw.mit.edu/courses/physics/8-02sc-physics-ii-electricity-and-magnetism-fall-2010/electric-fields/electric-fields-and-discrete-charge-distributions/ In the end the is a formula, which answers your question. Those cos/sines show direction, not a distance r, and they are not just multiplied (there is a minus i vector) in the formula.