Average Effective Dipole moment

Apr 2013
1. The problem statement, all variables and given/known data
(Bold x is the unit vector)

A.Water relative permitivity is about 81. If the electric field E=1.0 x[V/m] is inside the water, what is the vector P(dipole polarization per unit volume)?

B.Assume that the density of water is 1000 [kg/m3]
and that there are 3.34 × 1025 molecules per kg of water. (One mole of water weighs 18.0[g] since atomic weight of water is 18.0. A mole contains a number of molecules that is equal to Avogadro number (6.02 × 10^23)).
Determine an average effective dipole moment of each water molecule when E= 1.0 x [V/m].
Note: each molecule of water has dipole moment. The average dipole moment,
however, is zero since these dipole moments are randomly oriented. The average effectivedipole moment px is induced by the applied electric filed because the molecules are preferentially oreinted along the field.

C.Calculate the average dipole displacement angle theta (the angle between the x axis and the angle of the each dipole inside the water) when the E = 1.0x [V/m]

2. Relevant equations
X = eps - 1 and P=eps0*X*E
P=Nv(p) or P=1/ΔVƩ(p)

3. The attempt at a solution
A and B I assume are correct.

A.X=81-1 = 80

P=eps0*80 x

B.Then I did to find the effective dipole moment by doing
(80*eps0)/(Denisty of water * # of molecules)

2.119e-38 [C*m]

So I have:
Total dipole moment/Volume (P) = 80*eps0 x
Effective dipole moment (pv) = 2.119e-38 [C*m]
E field = 1.0 x [V/m]

How do I find the displacement angle for part C.??
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