For a helium atom the polarisability volume is

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric fields in matter · Electric fields in matter

Electricity, Magnetism and Electromagnetism, Ch Dielectrics: polarisation, bound charge and the displacement field

Problem

For a helium atom the polarisability volume is α/4πε0=0.205×10−30 m3\alpha/4\pi\varepsilon_0 = 0.205\times10^{-30}\ \mathrm{m^3}, where α\alpha is defined by p=αE\mathbf{p} = \alpha\mathbf{E}. A helium atom sits in a uniform electric field of magnitude 2.5×106 V m−12.5\times10^{6}\ \mathrm{V\,m^{-1}}. Model the atom as a nucleus plus a cloud carrying the charge of its two electrons, and treat the whole cloud as shifting rigidly, so that p=2edp = 2ed where dd is the shift. Take the radius of the atom as 3.1×10−11 m3.1\times10^{-11}\ \mathrm{m}. ((a)) Estimate the induced dipole moment pp. ((b)) Estimate the shift dd of the electron cloud. ((c)) Express dd as a fraction of the atomic radius.

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