A molecule of water vapor causes an electricfield in the surrounding space as if
ID: 2165871 • Letter: A
Question
A molecule of water vapor causes an electricfield in the surrounding space as if it were an electricdipole.
a.) Derive an expression for the electric fielddue to an electric dipole at a point P at a distance z from thecenter of the dipole. The point P is along the dipoleaxis.
b.) If the dipole moment has a magnitude of6.2*10^-30 C.m, what is the magnitude of the electric field at adistance 1.1 nanometer from the molecule on its dipole axis? Note:the distance z is large compared to the charge separationd.
Explanation / Answer
a) E = E(q) + E(-q) E = 2E*sin(theta) E = 2*(q/kz^2)*sin(theta) for z >>> d E = 2*(q/kz^2)*(0.5d/z) E = qd/kz^3 E = p/kz^3 where p is the electric dipole moment and k is 1/(4pi*epsilon) = 9*10^9 b) E = (6.2*10^-30)*(9*10^9)/(1.1*10^-9)^3 E = 41.92 * 10^6 V/m