Homework Help: Dipole pair electric field

1. The problem statement, all variables and given/known data

assume that two dipoles are placed back -t0 - back along axis as shown:




((-) a (+))(( +) a (-)) ------------------x axis


r is oriented between ))(( but above, a distance such that r>>a




compute the strength of the electric field on the axis of the pair at a distance r away from the the center of the dipole pair. use the approximation r>>a to simply your expression. each charge can be assumed to be 1 microcoulomb charge with the sign shown in the diagram

2. Relevant equations

electric potential V = kq/r where k is 9*10^9 constant, q is charge in coulombs, r is distance the charge is from the point r

electric field E = 2kP/r^3 where P is the dipole moment, given as 10^-8 C-m -->derivative of electric potential eq


3. The attempt at a solution

i am not sure where to draw the diagram as shown with lines connecting each charge (4 of them) and using the V equation to sum them up, but r is not given a numeric value

then do i do the derivative of the summation of V?

or do i just use the electric field equation, but how do i involve all four charges, and what do i put in for r in the denominator?

any help appreciated

cheers...

 

sorry for double posting, but i think i may have the wrong electric potential V equation.

should it be:

V =kpcosine(theta)/r^2 where p = 2qa, q = charge, a is distance b/w charges of dipole.

but since the problem involves two dipoles, do i multiply V by 2? how about the derivative (electric field E)?

but in order to find the electric field, i would need to take the derivative, so i should get this:

E = 2kpcosine(theta)/r^3 where r is the distance between pt r and the dipole(s)

do i multiply E by two because the problem involves two dipoles? when i put in p = 2qa with q = 1 microcoulomb and r>>a i got

E = 72000a(cosine(theta))/r^3 newtons/coulomb

any closer?...