Case: Read the passage and answer the question.
Conductors contain mobile charge carriers. In metallic conductors, these charge carriers are electrons. In a metal, the outer (valence) electrons part away from their atoms and are free to move. These electrons are free within the metal but not free to leave the metal. The free electrons form a kind of ‘gas’; they collide with each other and with the ions and move randomly in different directions. In an external electric field, they drift against the direction of the field. The positive ions made up of the nuclei and the bound electrons remain held in their fixed positions. A dielectric (an insulator) behaves differently. Its charges are held to their atoms or molecules and cannot move freely through it. An external electric field can only shift these charges a little or turn the molecules. The dielectric is then said to be polarised.
Unlike a metal, a dielectric has almost no free charge carriers. In a slab of a linear isotropic dielectric of electric susceptibility \( \chi_e=2 \), the electric field is \(5\times10^{4}\ \mathrm{V\,m^{-1}}\). What is the polarisation of the slab? (Take \(\varepsilon_0=8.85\times10^{-12}\ \mathrm{C^{2}\,N^{-1}\,m^{-2}}\).)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(8.85\times10^{-7}\ \mathrm{C\,m^{-2}}\)
Polarisation is the dipole moment per unit volume of a dielectric. For a linear isotropic dielectric, it is proportional to the field inside it, \( P=\varepsilon_0\chi_eE \).
Given:
\( \chi_e=2 \)
\( E=5\times10^{4}\ \mathrm{V\,m^{-1}} \)
\( \begin{aligned} P &= \varepsilon_0\chi_eE \\ &= 8.85\times10^{-12}\times2\times5\times10^{4} \\ &= 8.85\times10^{-7}\ \mathrm{C\,m^{-2}} \end{aligned} \)
NCERT (2026-27):
Dielectrics and Polarisation – “The dipole moment per unit volume is called polarisation and is denoted by P. For linear isotropic dielectrics,”
\( P=\varepsilon_0\chi_e E \)\( \qquad (2.37) \)
“where χe is a constant characteristic of the dielectric and is known as the electric susceptibility of the dielectric medium.”