# Dipole and electrostatics

1. Mar 11, 2009

### Dell

given a dipole as in the diagram (http://picasaweb.google.com/devanlevin/DropBox?authkey=Gv1sRgCL_4l4PpvP_YsQE#5311991019489958690 [Broken]) with charges of +q and -q placed a distance of "d" from one another.
a) what is the electric field at point z, on a line 90 degrees to the middle of the dipole?
b)what is the electric field at point z, on a line 90 degrees to the middle of the dipole when z>>d? (use the taylor series -> f(x)=f(0)+(1/1!)f'(0)+(1/2!)f''(0)... x<<1)

for a)

the distace from each charge to z is r=[(0.5d)2+z2]0.5
let alpha be the angle between the field of each charge and the horizontal z line,
sin(alpha)= (0.5d)/r= d/2[(0.5d)2+z2]0.5

for my x axis i can see that my field will be 0 since E1x=-E2x
Ey=[K(q/r2)+K(q/r2)]sin(alpha)

Ey=(2kq/[(0.5d)2+z2])*(d/2=[(0.5d)2+z2]0.5)

E=kqd/[(0.5d)2+z2]1.5

now for b) it is clear that if z>>d then d has no real meaning in the denominator so E=kqd/z3 but how do i prove this using the taylor series

Last edited by a moderator: May 4, 2017