actually, doing the whole thing from the electric field is ridiculously stupid. I realized I should start it in Volts so it looks like this
V = \frac{q}{4\pi\epsilon} (\frac{1}{r-\frac{l}{2}cos\vartheta}-\frac{1}{r+\frac{l}{2}cos\vartheta}) which then simplifies to...
Ok. but my biggest problem is then simplifying the numerator, and I tried using binomial expansion for that and you get (x^{2}+z^{2}+dz)^{3/2} - (x^{2}+z^{2}-dz)^{3/2} and a denominator of (x^{2} + z^{2})^{3}
sorry to ask but what do you do from there?
Homework Statement
The problem is: Show that the components of \vec{E} due to a dipole are given at distant points, by Ex=\frac{1}{4\pi\epsilon{o}} \frac{3pxz}{(x^2+z^2)^{5/2}} and Ez=\frac{1}{4\pi\epsilon{o}} \frac{p(2z^2-x^2)}{(x^2+z^2)^(\frac{5}{2})}}...
Homework Statement
The problem is: Show that the components of \vec{E} due to a dipole are given at distant points, by Ex=\frac{1}{4\pi\epsilon{o}} \frac{3pxz}{(x^2+z^2)^{5/2}} and Ez=\frac{1}{4\pi\epsilon{o}} \frac{p(2z^2-x^2)}{(x^2+z^2)^(5/2)}}...