NCERT Solutions for Chapter: Electrostatic Potential and Capacitance, Exercise 4: LA

A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage $V$ as $\mathrm{\epsilon }=\alpha V$ where $\alpha =2{\mathrm{V}}^{-1}$. A similar capacitor with no dielectric is charged to $78\mathrm{V}$. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.

A capacitor is made of two circular plates of radius $R$ each, separated by a distance $d<<R$. The capacitor is connected to a constant voltage. A thin conducting disc of radius $r<<R$ and thickness $t<<r$ is placed at a centre of the bottom plate. Find the minimum voltage required to lift the disc if the mass of the disc is $m$

In a quark model of elementary particles, a neutron is made of one up quarks [charge $(2/3) \mathrm{e}$] and two down quarks [charges $-(1/3) \mathrm{e}$]. Calculate the electrostatic potential energy of the neutron and compare it with its mass $939 \mathrm{MeV}.$ Repeat the above exercise for a proton which is made of two up and one down quark.

Two metal spheres, one of radius $\mathrm{R}$ and the other of radius $2\mathrm{R}$, both have same surface charge density$\sigma$ . They are brought in contact and separated. What will be the new surface charge densities on them?

In the circuit shown in Figure initially ${\mathrm{K}}_1$ is closed and ${\mathrm{K}}_2$ is open. What are the charges on each capacitors. Then ${\mathrm{K}}_1$ was opened and ${\mathrm{K}}_2$ was closed (order is important), What will be the charge on each capacitor now? $[\mathrm{C}=1\mathrm{\mu F}]$

Calculate potential on the axis of a disc of radius $\mathrm{R}$ due to a charge $\mathrm{Q}$, uniformly distributed on its surface.

Two charges ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$ are placed at $(0,0,\mathrm{d})$ and $(0, 0, -\mathrm{d})$ respectively. Find locus of points where the potential a zero.

Two charges $-q$ each are separated by distance $2d$. A third charge $+q$ is kept at mid point $O$. Find potential energy of $\mathit{+}q$ as a function of small distance $x$ from $\mathrm{O}$ due to $-q$ charges. Sketch P.E. $v/s x$ and convince yourself that the charge at $\mathrm{O}$ is in an unstable equilibrium.