A dielectric slab has a face area of 50 cm2 and a thickness of 4 mm. It is placed in a uniform electric field and gets uniformly polarised. Its net dipole moment is \(6\times10^{-10}\ \mathrm{C\,m}\). The polarisation of the slab is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(3\times10^{-5}\ \mathrm{C\,m^{-2}}\)
Polarisation \( P \) is the dipole moment per unit volume. For a slab that is uniformly polarised, it is the net dipole moment divided by the volume of the slab.
Given:
\( p=6\times10^{-10}\ \mathrm{C\,m} \)
\( A=50\ \mathrm{cm^{2}}=5\times10^{-3}\ \mathrm{m^{2}} \)
\( t=4\ \mathrm{mm}=4\times10^{-3}\ \mathrm{m} \)
\( \begin{aligned} V &= At \\ &= 5\times10^{-3}\times4\times10^{-3} \\ &= 2\times10^{-5}\ \mathrm{m^{3}} \end{aligned} \)
\( \begin{aligned} P &= \frac{p}{V} \\ &= \frac{6\times10^{-10}}{2\times10^{-5}} \\ &= 3\times10^{-5}\ \mathrm{C\,m^{-2}} \end{aligned} \)
NCERT (2026-27):
Dielectrics and Polarisation – “… The dipole moment per unit volume is called polarisation and is denoted by P. …”
Dielectrics and Polarisation – “… The field causes a uniform polarisation P of the dielectric. Thus … every volume element Δv of the slab has a dipole moment P Δv in the direction of the field.”