Reference no: EM13963016

Consider a dipole consisting of two charged particles on the x axis, one with positive charge q+ located at x=+1/2d and one with negative q- charge located at x=-1/2d

a) Derive an exact expression for the three dimensional potential field created by this dipole at a point P whose coordinates are {x, y, and z}

b) Use the binomial approximation to show that for points who distance r from the origin is very large compare to d, the electric potential is approximately given by

(x,y,z)=(kqd/r^2)(x/r)=(kqd/r^2)(cos)
where (cos) =x/r is the angle that the position vector of point P makes with the x axis. Note that the potential of a dipole falls off as 1/r^2 compared to 1/r for a point charge.

Note also that it is a lot easier to compute the electric field of a dipole using this formula that it is to calculate the field directly.