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

Define an equipotential surface.

On increasing the potential difference of a $8$ micro-farad capacitor from $20$ volt to $25$ volt, calculate the increase in its potential energy.

The plates of a parallel plate capacitor have an area $100 {\mathrm{cm}}^2$ each and are separated by $0.025 \mathrm{cm}$. What will be the potential difference between the plates if $3.54 \mathrm{\mu C}$ charge is supplied to the capacitor? What will be the new potential difference if the plate separation is increased to $0.05 \mathrm{cm}$?

A point charge of $3 \mathrm{\mu C}$ is placed at the origin of $\mathrm{X}-\mathrm{Y}$ coordinate system. Find out the potential difference between the points $\mathrm{A}\left(5\mathrm{a}, 0\right) \mathrm{and} \mathrm{B}\left(-3\mathrm{a}, 4\mathrm{a}\right)$.

The area of each plate of a parallel plate capacitor is $\mathrm{A}$ and separation between them is $\mathrm{d}$. As shown in the figure, slabs of dielectric constants ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are placed in between the plates, Find out the capacitance of the capacitor.

Four point charges $\mathrm{Q}, \mathrm{q}, \mathrm{Q}$ and $\mathrm{q}$ are placed at the corners of a square of side $a$ as shown in the figure.

Find

$\left(\mathrm{ii}\right)$ electrical potential energy of the system.

On which factors, does the capacitance of a parallel plate capacitor depend ? A parallel plate air capacitor is of $3 \mathrm{pF}$capacitance. When a plate of dielectric constant $\mathrm{k}$and thickness $\raisebox{1ex}{$3\mathrm{d}$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ is placed between the plates of the capacitors the capacitance of the capacitor becomes $6 \mathrm{pF}$. Find the magnitude of $\mathrm{k}$, where $\mathrm{d}$$\mathrm{is}$ the distance between the plates of the capacitor.

what is Coulomb's law of electric force ? Three point charges $+\mathrm{q}, -4\mathrm{q}$and $+2\mathrm{q}$ are placed at the vertices of an equilateral triangle of sides $1$, as shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge $+\mathrm{q}$. Also find out the work done to separate the charges in order to move them up to infinity.