Why is the average moment of a dipole zero?

[MathematicalPhysicist]

let's say we have an electron circling the nucleus (like the bohr's hydrogen atom), i don't understand why the average wrt to time of the moment of the diople is zero?
we have this equation: $$\frac{\int_{0}^{T}pdt}{T}$$
well obviously the diople, p, is constant throughout the elctron's motion, and it ahs the value p=eR where e is the electro's charge and R is the radius of motion, so unless I am missing something the average should be eR, so why am i wrong here?

thanks in advance.

 

[christianjb]

The dipole is a vector.

 

[MathematicalPhysicist]

i know that it's defined as a vector which its direction is along the radius, does it mean that on the whole circle the vectors cancel each other, obviously they do.
thanks.

 

[christianjb]

i know that it's defined as a vector which its direction is along the radius, does it mean that on the whole circle the vectors cancel each other, obviously they do.
thanks.

Yes. The atom has an instantaneous, but not a permanent dipole.