Discussion
When a monoatomic gas atom is placed in a uniform electric field, the resulting induced dipole moment is :
Answer: A
The induced dipole moment is proportional to E.
A field pulls the electron cloud of a neutral atom one way and the nucleus the other until the restoring force balances the applied force. For ordinary fields the displacement is proportional to the field, so
\[ \vec{p} = \alpha\vec{E} \]
where \(\alpha\) is the atomic polarizability. A simple model of the atom as a point nucleus in a uniform sphere of charge gives \(\alpha = 4\pi\varepsilon_{0}R^{3}\).
Terms in \(E^{2}\) or \(E^{3}\) appear only as small non-linear corrections at very strong fields, and a monoatomic atom has no permanent dipole moment, so the induced moment is not independent of E.
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