Class 12 Physics NCERT Solutions Chapter 2: Electrostatic Potential and Capacitance - Important Questions

The Class 12 Physics NCERT textbook is essential for students preparing for their board exams and competitive exams like JEE and NEET. Chapter 2, "Electrostatic Potential and Capacitance," is a crucial chapter that deals with the concepts of electrostatics, electric potential, potential energy, and capacitance. Understanding these concepts thoroughly is essential for mastering the topics related to electric fields and circuits. This article covers important questions from Chapter 2 to help students prepare effectively.

Understanding Chapter 2: Electrostatic Potential and Capacitance

Before we dive into the important questions, it is essential to have a quick overview of the key topics covered in this chapter:

1. Electrostatic Potential: The work done in moving a unit positive charge from infinity to a point in an electric field.
2. Electrostatic Potential Difference: The difference in electric potential between two points in an electric field.
3. Equipotential Surfaces: Surfaces where every point has the same electric potential.
4. Relation Between Electric Field and Potential Gradient: Electric field as the negative gradient of electric potential.
5. Potential Due to a Point Charge, Dipole, and System of Charges: Calculating potential for various charge distributions.
6. Electric Potential Energy of a System of Charges: Work done in assembling a system of charges.
7. Conductors and Dielectrics in Electrostatics: Behavior of conductors and dielectrics in an electric field.
8. Capacitance of a Capacitor: The ability of a system to store electric charge.
9. Capacitors in Series and Parallel: Calculation of equivalent capacitance in different combinations.
10. Energy Stored in a Capacitor: The energy stored in a charged capacitor.
11. Dielectrics and Polarization: Role of dielectrics in capacitors and their effect on capacitance.

With these key topics in mind, let's delve into the important questions that students must practice to excel in their exams.

Important Questions and Solutions from Chapter 2

1. What is Electrostatic Potential and Potential Difference?

• Question: Define electrostatic potential at a point and electrostatic potential difference between two points. How are they related to the work done in moving a charge in an electric field?

• Answer: The electrostatic potential (V) at a point in an electric field is defined as the amount of work done in moving a unit positive charge from infinity to that point against the electric field. Mathematically, it is expressed as:

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

  where $W$ is the work done and $q$ is the charge.

  The electrostatic potential difference (ΔV) between two points $A$ and $B$ in an electric field is the work done in moving a unit positive charge from point $A$ to point $B$. It is given by:

  $$\Delta V = V_B - V_A$$

  The relation between the electric field $E$ and the potential difference is given by:

  $$E = -\frac{dV}{dx}$$

  where $dV/dx$ is the potential gradient.

2. Derive the Expression for the Potential Due to a Point Charge.

• Question: Derive the expression for the electric potential at a distance $r$ from a point charge $q$.

• Answer: The electric potential $V$ at a distance $r$ from a point charge $q$ is given by:

  $$V = \frac{1}{4 \pi \varepsilon_0} \frac{q}{r}$$

  where $\varepsilon_0$ is the permittivity of free space. This is derived by considering the work done in moving a unit positive charge from infinity to a distance $r$ from the point charge against the electric field created by the point charge.

3. Explain Equipotential Surfaces. Give an Example.

• Question: What are equipotential surfaces? Explain with an example and describe the properties of equipotential surfaces.

• Answer: Equipotential surfaces are surfaces on which every point has the same electric potential. Since the potential difference between any two points on an equipotential surface is zero, no work is done in moving a charge from one point to another on the same surface.

  An example of an equipotential surface is a concentric spherical shell around a point charge. For a point charge, the equipotential surfaces are spherical, centered around the charge.

  Properties of Equipotential Surfaces:

  • The electric field is always perpendicular to the equipotential surface.
  • No work is required to move a charge along an equipotential surface.
  • Equipotential surfaces never intersect.

4. How is the Electric Potential Related to the Electric Field?

• Question: Derive the relationship between electric field $E$ and electric potential $V$.

• Answer: The electric field $E$ is related to the electric potential $V$ by the negative gradient of the potential. Mathematically,

  $$E = -\frac{dV}{dx}$$

  In three dimensions, this is represented as:

  $$\vec{E} = -\nabla V$$

  This equation shows that the electric field points in the direction of the steepest decrease in electric potential.

5. Calculate the Potential Energy of a System of Charges.

• Question: Derive the expression for the electrostatic potential energy of a system of two point charges $q_1$ and $q_2$ separated by a distance $r$.

• Answer: The electrostatic potential energy $U$ of a system of two point charges $q_1$ and $q_2$ separated by a distance $r$ is given by:

  $$U = \frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r}$$

  This expression is derived by calculating the work done in bringing charge $q_2$ from infinity to a distance $r$ from charge $q_1$ against the electric field due to $q_1$.

6. What is Capacitance? Derive the Capacitance of a Parallel Plate Capacitor.

• Question: Define capacitance. Derive the expression for the capacitance of a parallel plate capacitor with a dielectric medium between the plates.

• Answer: Capacitance (C) is defined as the ability of a system to store electric charge per unit potential difference. It is given by:

  $$C = \frac{Q}{V}$$

  where $Q$ is the charge stored, and $V$ is the potential difference across the plates.

  For a parallel plate capacitor with plates of area $A$ separated by a distance $d$, and a dielectric medium of dielectric constant $K$ between them, the capacitance is given by:

  $$C = \frac{K \varepsilon_0 A}{d}$$

  where $\varepsilon_0$ is the permittivity of free space.

7. Explain the Effect of a Dielectric on the Capacitance of a Capacitor.

• Question: How does the insertion of a dielectric material between the plates of a capacitor affect its capacitance?

• Answer: The insertion of a dielectric material between the plates of a capacitor increases its capacitance. The dielectric reduces the effective electric field between the plates, allowing the capacitor to store more charge for the same potential difference. The capacitance $C'$ with a dielectric of dielectric constant $K$ is given by:

  $$C' = K \times C$$

  where $C$ is the capacitance without the dielectric.

8. Derive the Expression for the Energy Stored in a Capacitor.

• Question: Derive the expression for the energy stored in a capacitor of capacitance $C$ charged to a potential $V$.

• Answer: The energy $U$ stored in a capacitor is given by:

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

  This is derived by calculating the work done in charging the capacitor from zero to potential $V$.

9. Explain the Series and Parallel Combination of Capacitors.

• Question: What is the equivalent capacitance of capacitors in series and parallel?

• Answer: For capacitors in series, the reciprocal of the equivalent capacitance $C_{\text{eq}}$ is the sum of the reciprocals of the individual capacitances:

  $$\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \ldots$$

  For capacitors in parallel, the equivalent capacitance $C_{\text{eq}}$ is the sum of the individual capacitances:

  $$C_{\text{eq}} = C_1 + C_2 + \ldots$$

10. Discuss the Concept of Polarization in Dielectrics.

• Question: What is polarization in dielectrics? How does it affect the capacitance of a capacitor?

• Answer: Polarization in dielectrics refers to the alignment of electric dipoles within the dielectric material in response to an external electric field. This alignment creates an induced electric field that opposes the external field, reducing the overall field within the capacitor and thus increasing the capacitance.

Conclusion

The important questions covered in this article provide a comprehensive understanding of the key concepts in Chapter 2, "Electrostatic Potential and Capacitance," from the Class 12 Physics NCERT textbook. By thoroughly understanding these questions and their solutions, students can solidify their understanding of electrostatics, which is crucial for both board exams and competitive exams like JEE and NEET. Practice these questions diligently and refer to NCERT solutions for a deeper grasp of the concepts.