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# NCERT Solutions for Class 12 Physics Chapter 2 - Electrostatic Potential And Capacitance – Free PDF Download

NCERT Solutions for Class 12 Physics Chapter 2 Electrostatic Potential and Capacitance includes the usage of many complicated equations and formulas that you can learn in your Class 12. Also, the PDF file of this chapter 2 Electrostatic Potential and Capacitance NCERT solutions is available here on our website for free, you can download them and use them without the internet. This PDF includes important questions, answers to questions from the textbook.

Further, the NCERT Solutions for Class 12 Physics Chapter 2 Electrostatic Potential and Capacitance provided here can be used by students to understand the concepts which are discussed in the chapter in detail.

## Subtopics of Class 12 NCERT Physics Chapter 2 – Electrostatic Potential and Capacitance

2.1 Introduction

2.2 Electrostatic Potential

2.3 Potential Due to a Point Charge

2.4 Potential Due to an Electric Dipole

2.5 Potential Due to a System of Charges

2.6 Equipotential Surfaces

2.6.1 Relation Between Field and Potential

2.7 Potential Energy of a System of Charges

2.8 Potential Energy in an External Field

2.8.1 Potential Energy of a Single Charge

2.8.2 Potential Energy of a System of Two Charges in an External Field

2.8.3 Potential Energy of a Dipole in an External Field

2.9 Electrostatics of Conductors

2.10 Dielectrics and Polarization

2.11 Capacitors and Capacitance

2.12 The Parallel Plate Capacitor

2.13 Effect of Dielectric on Capacitance

2.14 Combination of Capacitors

2.14.1 Capacitors in Series

2.14.2 Capacitors in Parallel

2.15 Energy Stored in a Capacitor

### Electrostatic Potential

Let us consider any general static charge configuration. We define potential energy of a test charge q in terms of the work done on the charge q. This work is directly proportional to charge q, since the force at any point is qE, where E is the electric field at that point due to the given charge configuration. It is, therefore, convenient to divide the work by the amount of charge q, so that the overall quantity is independent of charge q.

### Potential Due to a Point Charge

Consider a point charge Q at the origin point and take Q to be as positive charge. Here we will determine the potential at any point P with position vector r from the origin. For that we can calculate the work done in bringing a unit positive test charge from infinity to the point P. For Q > 0, the work done against the repulsive force on the test charge is always positive. Since work done is independent of the path, we choose a convenient path – along the radial direction from infinity point to the point P.

### Potential Due to an Electric Dipole

An electric dipole consists of two charges +q and  –q which is separated by a small distance 2a. Its total charge is zero. It is defined by a dipole moment vector p whose magnitude is q × 2a and which points in the direction from –q to q. We have seen that the electric field of a dipole at a point with position vector r depends not only on the magnitude r, but also on the angle between r and p.

### Potential Due to a System of Charges

Let us consider a system of charges q1, q2,…, qn with position vectors r1, r2,…, rn relative to some origin. The potential V1 at P due to the charge q1 and so on.

By the superposition principle, the potential V at P due to the total charge configuration is the algebraic sum of the potentials due to the individual charges

### Equipotential Surfaces

An equipotential surface is the contact points in space having the same potential at every point of surface. It means that a charge will have the same potential energy at every point on the surface.

#### Relation Between Field and Potential

Consider two closely spaced equipotential surfaces one is A and another is B with potential values V and V + d V, where d V is the change in V i.e potential values in the direction of the electric field E. Let P be a point on the surface B and d l is the perpendicular distance of the surface A from P. Let us consider that a unit positive charge is moved along this perpendicular from the surface B to surface A against the electric field.

### Potential Energy of a System of Charges

Let us consider first the simple case of two charges q1 and q2 with position vectors r1 and r2 relative to some origin point. Now calculate the external work done in building up this configuration. This means that we consider the charges q1 and q2 initially at infinity and determine the work done by an external body to bring the charges to the given locations. Assume that, first charge q1 is brought from infinity to the point r1. There is no external field against which work needs to be done, so work done in bringing q1 from infinity to r1 is zero.

### Potential Energy in an External Field

The external field E is not produced by the given charge or charges whose potential energy we want to calculate. E is produced by external sources to the given charge(s).The external sources may be known, but often they are unspecified or unknown; what is specified is the electric field E or the electrostatic potential V due to the external sources.

#### Potential Energy of a System of Two Charges in an External Field

The potential energy of charge q in the electric field is equal to the work done in gaining that charge from infinity. The potential energy of a single charge (q) at a distance r from the origin point is given by: qV(r), whereas V(r) is the external potential at a particular given point.

### Potential Energy of a Dipole in an External Field

Electric potential energy of an Electric dipole in an external field from zero energy position to the particular given position.

### Electrostatics of Conductors

The free electrons form a kind of ‘gas’ and they collide with each other and with the ions, and move freely in random directions. When an external electric field is applied, they drift against the direction of the electric field. The positive ions are made up of the nuclei and the bound electrons remain held in their fixed positions. In electrolytic conductors, the charge carriers are both positive charge and negative charge but the situation in this case is more involved – the movement of the charge carriers is affected both by the external electric field and as well as by the so-called chemical forces.

### Dielectrics and Polarization

Dielectric polarization happens when an external electric field is applied to a dielectric material. When an electric field is applied, it causes both positive charge and negative charge to be displaced. The primary goal of dielectric polarization is to connect microscopic and macroscopic characteristics.

### Capacitors and Capacitance

A capacitor is a system of two conductors and they are separated by an insulator. The conductors have charges, Q1 and Q2, and potentials are V1 and V2. Geneally, in practice, the two conductors have charges +Q and – Q, with potential difference V = V1 – V2 between them. The conductors may be charged by connecting them to the two terminals with a battery where Q is called the charge of the capacitor, is the charge on one of the conductors – the total charge of the capacitor is zero.

The electric field in the region of the conductors is proportional to the charge Q. That means, if the charge on the capacitor is doubled, the electric field will also be doubled at every point because they are directly proportional.

### The Parallel Plate Capacitor

When two parallel plates are connected with a battery, the plates are charged and an electric field is established between the plates, and this setup is called the parallel plate capacitor.

### Effect of Dielectric on Capacitance

The strength of the electric field is reduced because of the presence of dielectric. If the total charge on the plates is constant, then the potential difference is reduced over the capacitor plates. In this manner, dielectric increases the capacitance of the capacitor.

### Combination of Capacitors

Basically, there are two types of combinations of capacitors, one is series and another is parallel combinations of the capacitor. In a series combination of capacitors, each capacitor is connected one after another. On the other side, the two plates are arranged in parallel with dielectric material in between in a parallel capacitor.

#### Capacitors in Series

When capacitors are connected one after one, they are a known series combination of capacitors. For capacitors in series, the total capacitance can be found by adding the reciprocals of the individual capacitances, and taking the reciprocal of the sum of the capacitors.

#### Capacitors in Parallel

When capacitors are connected in parallel, the total capacitance is the sum of the capacitances of the individual capacitors. When two or more capacitors are connected in parallel, the total capacitance is that of a single equivalent capacitor having the sum of the plate areas of the individual capacitors.

### Energy Stored in a Capacitor

Energy stored in a capacitor is known as electrical potential energy, and it is related to the charge Q and voltage V on the capacitor.

## Important Points of NCERT Class 12 Physics Chapter 2 – Electrostatic Potential and Capacitance

Following are the important points of NCERT class 12 Physics Chapter 2 – Electrostatic Potential and Capacitance

• Equipotential surfaces.

• Potential due to electric dipole and system of charges.

• Electric potential energy due to electric dipole and system of charges.

• Effect of dielectric on capacitors.

• Energy stored in capacitors.

• Combinations of capacitors.

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• All the solutions provided in the PDF are absolutely correct & of very high quality.

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#### FAQs

Question 1 : What are the main topics and subtopics covered in Chapter 2 of NCERT Solutions for Class 12 Physics?

Answer: The main topics and sub-topics covered in Chapter 2 of NCERT Solutions for Class 12 Physics are mentioned below:

2.1 Introduction

2.2 Electrostatic Potential

2.3 Potential Due to a Point Charge

2.4 Potential Due to an Electric Dipole

2.5 Potential Due to a System of Charges

2.6 Equipotential Surfaces

2.6.1 Relation between Field and Potential

2.7 Potential Energy of a System Of Charges

2.8 Potential Energy in an External Field

2.8.1 Potential Energy of a Single Charge

2.8.2 Potential Energy of a System of Two Charges in an External Field

2.8.3 Potential Energy of a Dipole in an External Field

2.9 Electrostatics of Conductors

2.10 Dielectrics and Polarization

2.11 Capacitors and Capacitance

2.12 The Parallel Plate Capacitor

2.13 Effect of Dielectric on Capacitance

2.14 Combination of Capacitors

2.14.1 Capacitors in Series

2.14.2 Capacitors in Parallel

2.15 Energy Stored in a Capacitor

Question 2: What is a series capacitor?

Answer: When capacitors are connected one after one, they are known as series capacitors.