1.

A non-polar molecule with polarzabillity `beta` is located at a great distance `l` from a polar molecule with electric moment `p`. Find the magnitude of the interaction force between the molecules if the vector `p` si oriented along a straight line passing through both molecules.

Answer» From the genral formula
`vec(E) = (1)/(4pi epsilon_(0)) (3 vec(p). vec(r ). vec(r ) - vec(p) r^(2))/(r^(5))`
`vec(E) = (1)/(4pi epsilon_(0)) (2vec(p))/(l^(3))`, where `r = l`, and `vec(r ) uarr uarr vec(p)`
This will cause the induction of a dipole moment.
`vec(p_("ind")) = beta (1)/(4pi epsilon_(0)) (2 vec(p))/(l^(3)) xx epsilon_(0)`
Thus the force,
`vec(F) = (beta)/(4pi ) (2p)/(l^(3)) (del)/(del l) (1)/(4pi epsilon_(0)) (2p)/(l^(3)) = (3 beta p^(2))/(4pi^(2) epsilon_(0) l^(7))`


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