Some types of molecules that do not possess an intrinsic electric dipole moment

Question

Some types of molecules that do not possess an intrinsic electric dipole moment can be given one by an external electric field in a process called charge separation, or polarization. In this process their internal charge distribution becomes distorted by the field, with the result that the region of a molecule on the side in the direction of the field gains a positive net charge, while the region on the other side gains a negative net charge. Both charges have equal magnitudes and the electric neutrality of the molecule as a whole is maintained. The electric field is said to induce an electric dipole moment in such a molecule. When the field is canceled, the molecule reverts to its unpolarized state and loses its electric dipole moment. Let us model the electric behavior of such a molecule by a pair of plusminus1.60 Times 10^-19-C charges connected by a spring with force constant 2.29 Times 10^-4 N/m. The spring must be imagined as possessing zero relaxed length so that normally the charges overlap and the molecule has zero dipole moment. In the presence of an electric field, however, the positive charge is pulled in the direction of the field, while the negative charge is pulled in the opposite direction. This charge separation endows the molecule with an electric dipole moment. Find the charge separation distance in an electric field of 7.63 Times 10^5 N/C. What is the magnitude of the induced electric dipole moment then?

Explanation / Answer

By Newton’s second law,

Fnet = ma

-kx + Fe = 0

kx = Fe

kx= qE

x= (qE)/k

x = (1.60*10^-19*7.63*10^5)/(2.29*10^-4) = 5.33*10^-10 m

P=qx = (1.60*10^-19)*( 5.33*10^-10) = 8.52*10^-28 Cm

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