Embibe Experts Solutions for Chapter: Electrostatic Potential and Capacitance, Exercise 1: Nagaland Board-2019

Establish a relationship between electric potential and electric field.

Two point charges of $+1.5 \mathrm{\mu C}$ and $+2.5 \mathrm{\mu C}$ are placed $30\mathrm{cm}$ apart. Calculate the magnitude of electric potential and electric field at the midpoint of the line joining the two charges.

Two charges of $+5\mathrm{nC}$and $-2\mathrm{nC}$ are placed at points $(5\mathrm{cm}, 0,0)$ and $(23\mathrm{cm}, 0,0)$ in a region of space where there is no other external electric field. Calculate potential energy of this charge system.

Three capacitors are connected as shown in the following figure. Calculate the resultant capacitance. If the combination is connected across a $30\mathrm{V}$ DC battery, find the total charge drawn by the arrangement.

Prove that total electrostatic potential energy stored in a capacitor is $\frac{1}{2}{\mathrm{CV}}^2$. Hence, derive an expression for the energy density of an electric field.

Derive an expression for electric potential due to a point charge. How do electric potential vary with distance $‘\mathrm{r}’$for a point charge?

A parallel plate capacitor with air between the plates has a capacitance of $8\mathrm{pF}(1\mathrm{pF} = {10}^{-12}\mathrm{F})$. What will be the capacitance of the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant $6$?

A $600 \mathrm{pF}$ capacitor is charged by a $200\mathrm{V}$ supply. It is then disconnected from the supply and is connected to another uncharged $600\mathrm{pF}$ capacitor. How much electrostatic energy is lost in the process?