NCERT Class 12 Physics Chapter 2 Notes - Electrostatic Potential and Capacitance

Ever wondered how a small capacitor can store and release energy in your electronic devices? Electrostatic potential and capacitance is the key to understanding how charges interact and how energy is stored. These class 12 notes simplify complex concepts, making revision easier for board exams, as well as for competitive exam like JEE and NEET.

To make revision easier, subject matter expert team from Careers360 has created class 12 physics chapter 2 notes, covering key concepts, and formulas. These notes help students grasp Electrostatic Potential and Capacitance quickly and effectively. Whether for class tests, board exams as well as for competitive exam like JEE, or NEET.

Also, students can refer,

• NCERT Solutions for Class 12 Physics Chapter 2 Electrostatic Potential and Capacitance
• NCERT Exemplar Class 12 Physics Chapter 2 Solutions Electrostatic Potential and Capacitance

Electric Potential:

The electrostatic potential in a region of the electric field is equal to the amount of work done in bringing a unit-positive test charge from infinity to that point against the electrostatic force.

$V=\frac{W}{q_0}$

Where,

W - work done and $q_0$ - unit charge

• Electric potential is a scalar quantity and the SI unit is Volt (V).
• CGS unit is stat-volt.
• Dimension - $M{L}^2{T}^{-3}{A}^{-1}$.

1 volt $=\frac{1}{300}$ stat volt.

Potential due to system of point charges:

$V=\sum _{i=1}^n\frac{K{Q}_i}{r_i}$

Potential difference:

The potential difference between two points A and B in an electric field is equal to the amount of work done (by an external agent) in moving a unit positive charge from point A to another point B.

$V_B-V_A=\frac{w}{q}$

Where,

W is the amount of work done and q is the unit positive charge.

Electric potential due to a point charge:

$\begin{array}{rl}& V=\frac{Kq}{r}\\ & K=\frac{1}{4\pi {ϵ}_0}\end{array}$

Potential Due to an Electric Dipole

In the previous chapter on electric charges and field, we have already calculated the electric field due to an electric dipole and seen that for an ideal (short) dipole, the electric field varies inversely as $r^3$, we now determine the potential due to an electric dipole.
$AB$ be an electric dipole of length $2a$ and let $P$ be any point where $OP=r$.
Let $\theta$ be the angle between $r$ and the dipole axis.

$AB=2a,AO=OB=a,OP=r$

$\text{ In }\mathrm{△}OAC,\cos \theta =\frac{OC}{OA}=\frac{OC}{a}$
$\therefore OC=a\cos \theta$

Also $OD=a\cos \theta$
If $r\gg a,PA=PC=OP+OC=r+a\cos \theta$

$PB\sim PD=OP-OD=r-a\cos \theta$

$V$ is the potential due to electric dipole.

$\begin{array}{rl}& V=\left(\frac{1}{4\pi x_0}\right)[\frac{q}{PB}-\frac{q}{PA}]\\ & V=\left(\frac{1}{4\pi x_0}\right)q[\frac{1}{(r-a\cos \theta )}-\frac{1}{(r+a\cos \theta )}]\\ & V=\left(\frac{1}{4\pi x_0}\right)\frac{2aq\cos \theta }{(r^2-a^2{\cos }^2\theta )}=\left(\frac{1}{4\pi x_0}\right)\frac{p\cos \theta }{(r^2-a^2{\cos }^2\theta )}\end{array}$

where $P$ is dipole moment.

Electric Potential Energy:

Consider a system with two charges, q₁ and q₂ fixed at points A and B, respectively, and separated by AB =r₂. If q₂ is moved from B to a new point C along AB and AC =r₂, and the charge is displaced from r to r + dr, then the work done (dW) is as follows:

dW=F.dr $=\frac{K{q}_1{q}_2}{r^2}\cdot dr$

• Total work done

$\begin{array}{rl}& W={\int }_{r_1}^{r_2}\frac{K{q}_1{q}_2}{r^2}\cdot dr\\ & =\frac{q_1{q}_2}{4\pi {ϵ}_0}[\frac{1}{r_1}-\frac{1}{r_2}]\end{array}$

• Change in potential energy

$\begin{array}{rl}& U\left(r_2\right)-U\left(r_1\right)=-W\\ & =\frac{q_1{q}_2}{4\pi {ϵ}_0}[\frac{1}{r_2}-\frac{1}{r_1}]\end{array}$

• When the system of two charges have infinite separation then potential energy

$U(\mathrm{\infty })=0$

• The potential energy when separation is r is

$\begin{array}{rl}& U(r{)}_0=U(r)-U(\mathrm{\infty })\\ & =\frac{q_1{q}_2}{4\pi {ϵ}_{0}r}\end{array}$

Equipotential Surface

An equipotential surface is a surface where the electric potential remains constant at every point. This means that no work is required to move a charge along this surface because the potential difference between any two points is zero.

• The electric field is always perpendicular to an equipotential surface.

• No work is done when moving a charge along an equipotential surface.

• In a uniform electric field, equipotential surfaces are parallel planes.

• For a point charge, equipotential surfaces are concentric spheres centered around the charge.

Relation Between Electric Field and Electric Potential:

If we know the electric potential in a region, we can find the electric field

$dV=-Edr\cos \theta$

where,

θ is the angle between E and dr

Electric Potential Due to a Dipole:

i) at the axial point

$V_{\text{arial }}=\frac{kP}{(r^2-l^2)}$

if $1\gg 1$

$V_{axi}=\frac{1}{4\pi {ϵ}_0}\frac{P}{r^2}$

ii) at the quatorial point:

$V_{\text{equi }}=0$

iii) General point

$V_g=\frac{1}{4\pi {ϵ}_0}\frac{P\cos \mathrm{\Theta }}{r^2}$

Work done in rotation of dipole and equilibrium of dipole:

$\begin{array}{rl}& W=PE(\cos {\mathrm{\Theta }}_1-\cos {\mathrm{\Theta }}_2)\\ & W=PE(\cos {\mathrm{\Theta }}_1-\cos {\mathrm{\Theta }}_2)\\ & \text{ if }{\theta }_1=90\text{ and }{\theta }_2=\theta \\ & W=-PE\cos \theta =-P.E\end{array}$

This work done is stored as potential energy.

Condition for the stable equilibrium of a dipole:

1. Angle (θ): The system is stable when the angle between the dipole moment (p) and the electric field (E) is 0° (aligned).

2. Torque: In this position, the net torque acting on the dipole is zero. Any slight deviation from this position causes a restoring torque, bringing the dipole back into alignment with the field.

3. Potential Energy: When the dipole is aligned with the electric field, its potential energy is at its lowest.

Condition for the unstable equilibrium of a dipole:

1. Angle (θ): The system is in unstable equilibrium when the angle between p and E is 180° (anti-aligned).

2. Torque: In this position, the net torque acting on the dipole is zero. Any small displacement from this position, however, produces a torque that increases the angle between p and E, pushing the dipole out of alignment.

3. Potential Energy: The dipole's potential energy is greatest when it is anti-aligned with the electric field.

Electrostatics of Conductors

• At electrostatic equilibrium, the electric field inside a charged conductor is zero.
• The electric field at every point on the surface of a charged conductor is normal (perpendicular) to the surface.
• In a static situation, the excess charge on a charged conductor exists only on its surface.
• There is no electric field inside the cavity of a conductor, providing electrostatic shielding.
• At electrostatic equilibrium, the electrostatic potential remains constant throughout the conductor.

Dielectrics and Polarization

• Dielectrics are non-conducting materials, and they do not have free charge carriers that can move easily within the material.

Non-Polar Molecules:

The centres of negative and positive charges coincide in a non-polar molecule. The non-polar molecule lacks a permanent dipole moment.

Example: O₂, H₂

Polar Molecule:

Polar molecules have negative and positive charge centres that are separated and have a permanent dipole moment.

Example: H₂O, HCl

NOTE : Both polar and non-polar dielectrics acquire a net dipole moment in the presence of an external electric field.

Polarization:

It is the dipole moment per unit volume

$P={\chi }_{e}E$

${\chi }_e$ is the electric susceptibility of the dielectric medium

• Polarized dielectrics are similar to two charge surfaces with an induced charge density of opposite polarity.

Capacitor

A capacitor is a system of two conductors, which are separated by an insulator. A capacitor is used to store a large amount of charge.

The charge stored in a capacitor:

$Q=CV$

where, C is capacitance and V is voltage

Capacitance (C):

The capacitance of a capacitor

$C=Q/V$

Dielectric Strength:

Dielectric strength is the maximum amount of electric field that a dielectric medium can withstand.

Parallel Plate Capacitor:

Two conducting plates of area A separated by a distance d. If the dielectric medium between the capacitor plate is vacuum or air, then

$C=\frac{{ϵ}_{0}A}{d}$

• When a dielectric of dielectric constant k is inserted between the above capacitor, the new capacitance

$\begin{array}{rl}& C^{\prime }=\frac{k{ϵ}_{0}A}{d}\\ & C^{\prime }=k\stackrel{C}{C}\end{array}$

Combination of capacitors:

Series Combination :

In series: $\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+$. $$
Note : In series combination equivalent capacitance is always less the smallest capacitor of combination.

Parallel Combination :

Equivalent capacitance of parallel combination ${\mathrm{C}}_{eq}={\mathrm{C}}_1+{\mathrm{C}}_2+{\mathrm{C}}_3$

Note : Equivalent capacitance is always greater than the largest capacitor of combination.

• For n capacitors connected in parallel, the net value of capacitance is

$C=C_1+C_2+C_3+\dots \dots \dots C_n$

• For n capacitors connected in series, the net value of capacitance is

$\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\dots \dots \dots \dots \dots \frac{1}{C_n}$

Energy Stored in a Capacitor:

The energy U stored in a capacitor of capacitance C, charge Q and voltage V is

$U=\frac{1}{2}C{V}^2$

The electric energy density

In a region with an electric field, the electric energy density,

Energy per unit volume $=\frac{1}{2}{ϵ}_0{E}^2$

A Van de Graaff Generator:

Van de Graaff generator is used for accelerating charged particles. It consists of a large spherical conducting shell. The charge is continuously transferred to the shell with the help of a moving belt and brushes. The potential of million volts rebuilt up and can be used for accelerating the charged particles.

Importance of NCERT Class 12 Physics Chapter 2 Notes

Class 12 Physics Chapter 2 notes on electrostatic potential and capacitances is very important to understand important concept and for quick revision. These notes cover important topics from the CBSE syllabus and are also very useful for competitive exams like JEE Main, NEET, BITSAT, and VITEEE. The NCERT-based notes help in grasping important formulas and concepts efficiently.

NCERT Class 12 Notes Chapterwise

Subject Wise NCERT Exemplar Solutions

• NCERT Exemplar Class 12 Solutions

• NCERT Exemplar Class 12 Maths

• NCERT Exemplar Class 12 Physics

• NCERT Exemplar Class 12 Chemistry

• NCERT Exemplar Class 12 Biology

Subject Wise NCERT Solutions

• NCERT Solutions for Class 12 Mathematics

• NCERT Solutions for Class 12 Chemistry

• NCERT Solutions for Class 12 Physics

• NCERT Solutions for Class 12 Biology

NCERT Books and Syllabus