Calculate the induced dipole moment per unit volume (polarization density) of helium gas when it is placed in a field of \(6 \times 10^{5} \mathrm{~V} / \mathrm{m}\). The atomic polarizability of helium is \(0.18 \times 10^{-40} \mathrm{Fm}^{2}\) and the concentration of helium atom is \(2.6 \times 10^{25} / \mathrm{m}^{3}\). Also calculate the separation of positive and negative charges in each atom. Ans. \(2.81 \times 10^{-10} \mathrm{C} / \mathrm{m}^{2}, 6.75 \times 10^{-17}\)

An electric field is a region around a charged particle where other particles experience a force. It is represented by the symbol \(E\) and measured in volts per meter (V/m). The strength of the electric field determines how strongly it can influence other charged particles.

In our problem, the value of the electric field is given as \(6 \times 10^5 \, \text{V/m}\). This means that any charged particle within this field will experience a force proportional to its charge and the electric field strength.

To calculate the induced dipole moment in helium gas, the electric field applies to the atomic polarizability of helium, altering the position of charges within the atoms.

Atomic polarizability describes how easily an atom's electron cloud can be distorted by an external electric field. It is denoted by the symbol \(\alpha\) and measured in farad meters squared (\text{Fm}^2).

In other words, it quantifies the extent to which an atom becomes polarized – with positive and negative charges separated – when subjected to an electric field.

For helium in our problem, the atomic polarizability is given as \(0.18 \times 10^{-40} \, \text{Fm}^2\). This value will be used with the electric field to calculate the induced dipole moment per helium atom, accounting for the displacement of charges within each atom.

Polarization density, symbolized as \(P\), is the measure of the dipole moment per unit volume of a material. It is influenced by the number density of the atoms and their dipole moments.

It is calculated using the formula:
\[ P = Np \]
where \(N\) is the concentration of atoms and \(p\) is the induced dipole moment per atom.

In our example, the concentration of helium atoms is \(2.6 \times 10^{25} \, /\text{m}^3\). Using the induced dipole moment per helium atom, we can calculate the polarization density, giving us insight into how a macroscopic volume of helium gas reacts to the electric field.

By multiplying the concentration and the induced dipole moment, we find the polarization density to be \(2.81 \times 10^{-10} \, \text{C}/\text{m}^2\), indicating the collective effect of the electric field on the helium gas.

Helium gas is a noble gas with atoms that are relatively hard to polarize due to their stable and compact electron structure. Helium atoms do not easily form bonds, making them unique compared to many other elements.

Due to its low atomic polarizability, the electron cloud of helium does not easily distort under an electric field. However, strong enough electric fields can still induce a small dipole moment in helium atoms, as shown in the problem.

Understanding helium's behavior under an electric field helps us grasp the interactions at an atomic level, providing a fundamental understanding of gas polarization and applications in fields like gas discharge physics and various technologies dependent on gas properties.