CBSE Class 12 · 2015 · ElectrostaticsLong Answer

(a) In a conductor, free charges move until the induced field exactly cancels the external field, so the net field inside is zero. In a dielectric there are no free charges; the molecules only polarise, setting up an opposing field that reduces, but does not cancel, the external field. Polarization $\vec{P}$ is the induced dipole moment per unit volume; for a linear dielectric $\vec{P}=\chi {\epsilon }_0\vec{E}$, where $\chi$ is the electric susceptibility. (b)(i) The field inside the shell (due to the shell's own charge) is zero, so the force on the central charge $\frac{Q}{2}$ is zero. For the external point A at distance $x$, the shell plus the central charge behave as a charge $Q+\frac{Q}{2}=\frac{3Q}{2}$ at the centre, so $F_A=\frac{1}{4\pi {\epsilon }_0}\frac{(2Q)(3Q/2)}{x^2}=\frac{3Q^2}{4\pi {\epsilon }_0{x}^2}$. (ii) Flux through the shell depends only on the charge enclosed by it, which is the central charge $\frac{Q}{2}$: $\varphi =\frac{Q/2}{{\epsilon }_0}=\frac{Q}{2{\epsilon }_0}$.