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

Electrostatic Potential and Capacitance is a core and high-weightage chapter in Class 12 Physics that builds on electrostatics. This chapter explains key concepts such as electrostatic potential and potential difference, equipotential surfaces, relation between electric field and potential, capacitors, capacitance of parallel plate capacitors, dielectrics, and energy stored in a capacitor. These topics are frequently asked in CBSE board exams and competitive exams like JEE and NEET.

NCERT Solutions for Class 12 Physics Chapter 2 – Electrostatic Potential and Capacitance are prepared strictly according to the latest CBSE syllabus and exam pattern. The solutions are written in simple, step-by-step language with clear derivations, diagrams, and solved numericals, helping students understand concepts thoroughly, practise effectively, and score well in board examinations.

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

Electrostatic Potential and Capacitance
Medium
Q.
Two charges 5 × 10−8 C and −3 × 10−8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
Electrostatic Potential and Capacitance
Medium
Q.
Two charged conducting spheres of radii a and b are connected to each other by a wire.
What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.
Electrostatic Potential and Capacitance
Medium
Q.
A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 μC. The space between the concentric spheres is filled with a liquid of dielectric constant 32.
(a) Determine the capacitance of the capacitor.
(b) What is the potential of the inner sphere?
(c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller.
Electrostatic Potential and Capacitance
Medium
Q.
A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig. 2.36). Show that the capacitance of a spherical capacitor is given by
C=4πε0r1r2r1−r2where r1and r2are the radii of outer and inner spheres, respectively.
Electrostatic Potential and Capacitance
Medium
Q.
The plates of a parallel plate capacitor have an area of 90 cm2 each and are separated by 2.5 mm. The capacitor is charged by connecting it to a 400 V supply.
(a) How much electrostatic energy is stored by the capacitor?
(b) View this energy as stored in the electrostatic field between the plates, and obtain the energy per unit volume u. Hence arrive at a relation between u and the magnitude of electric field E between the plates.
Electrostatic Potential and Capacitance
Medium
Q.
Obtain the equivalent capacitance of the network in Fig. 2.35. For a 300 V supply, determine the charge and voltage across each capacitor.
Electrostatic Potential and Capacitance
Medium
Q.
What is the area of the plates of a 2 F parallel plate capacitor, given that the separation between the plates is 0.5 cm? [You will realize from your answer why ordinary capacitors are in the range of 5F or less. However, electrolytic capacitors do have a much larger capacitance (0.1 F) because of very minute separation between the conductors.]
Electrostatic Potential and Capacitance
Medium
Q.
Figure 2.34 shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on r for r/a >> 1, and contrast your results with that due to an electric dipole, and an electric monopole (i.e., a single charge).
Electrostatic Potential and Capacitance
Medium
Q.
Two charges −q and +q are located at points (0, 0, − a) and (0, 0, a), respectively.
(a) What is the electrostatic potential at the points?
(b) Obtain the dependence of potential on the distance r of a point from the origin when r/a >> 1.
(c) How much work is done in moving a small test charge from the point (5, 0, 0) to (−7, 0, 0) along the x-axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?
Electrostatic Potential and Capacitance
Medium
Q.
In a hydrogen atom, the electron and proton are bound at a distance of about 0.53 Å:
(a) Estimate the potential energy of the system in eV, taking the zero of the potential energy at infinite separation of the electron from proton.
(b) What is the minimum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in (a)?
(c) What are the answers to (a) and (b) above if the zero of potential energy is taken at 1.06 Å  separation?
Electrostatic Potential and Capacitance
Medium
Q.
A spherical conductor of radius 12 cm has a charge of 1.6 × 10−7 C distributed uniformly on its surface. What is the electric field
(a) Inside the sphere
(b) Just outside the sphere
(c) At a point 18 cm from the centre of the sphere?
Electrostatic Potential and Capacitance
Medium
Q.
(a) Show that the normal component of electrostatic field has a discontinuity  from one side of a charged surface to another given by ( E → 2 − E → 1 )⋅ n ^  =  σ ε 0 Where,  ( n ^ )  is a unit vector normal to the surface at a point and σ is the surface  charge density at that point. (The direction of ( n ^ ) is from side 1 to side 2.)  Hence show that just outside a conductor, the electric field is σ n ^ ε 0 . (b) Show that the tangential component of electrostatic field is continuous from  one side of a charged surface to another. [Hint: For (a), use Gauss’s law. For, (b) use the fact that work done by electrostatic  field on a closed loop is zero.]
 
Electrostatic Potential and Capacitance
Medium
Q.
A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q.
(a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?
(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.
Electrostatic Potential and Capacitance
Difficult
Q.
Two tiny spheres carrying charges 1.5 μC and 2.5 μC are located 30 cm apart. Find the potential and electric field:
(a) at the mid-point of the line joining the two charges, and
(b) at a point 10 cm from this midpoint in a plane normal to the line and passing through the mid-point.
Electrostatic Potential and Capacitance
Medium
Q.
Explain what would happen if in the capacitor given in Exercise 2.8, a 3 mm thick mica sheet (of dielectric constant = 6) were inserted between the plates,
(a) While the voltage supply remained connected.
(b) After the supply was disconnected.
Electrostatic Potential and Capacitance
Difficult
Q.
In a parallel plate capacitor with air between the plates, each plate has an area of 6 ×10−3 m2 and the distance between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor?
Electrostatic Potential and Capacitance
Medium
Q.
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel.
(a) What is the total capacitance of the combination?
(b) Determine the charge on each capacitor if the combination is connected to a 100 V supply.
Electrostatic Potential and Capacitance
Medium
Q.
Three capacitors each of capacitance 9 pF are connected in series.
(a) What is the total capacitance of the combination?
(b) What is the potential difference across each capacitor if the combination is connected to a 120 V supply?
Electrostatic Potential and Capacitance
Medium
Q.
A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10−12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
Electrostatic Potential and Capacitance
Difficult
Q.
Answer carefully:
(a) Two large conducting spheres carrying charges Q1 and Q2 are brought close to each other. Is the magnitude of electrostatic force between them exactly given by Q1Q2/4πr 2, where r is the distance between their centres?
(b) If Coulomb’s law involved 1/r3 dependence (instead of 1/r2), would Gauss’s law be still true?
(c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?
(d) What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical?
(e) We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there?
(f) What meaning would you give to the capacitance of a single conductor
(g) Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (= 6).

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

Q. 1) Answer carefully:

(a) Two large conducting spheres carrying charges Q1 and Q2 are brought close to each other. Is the magnitude of electrostatic force between them exactly given by Q1Q2 / 4πr², where r is the distance between their centres?

(b) If Coulomb’s law involved 1/r³ dependence (instead of 1/r²), would Gauss’s law be still true?

(c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?

(d) What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical?

(e) We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there?

(f) What meaning would you give to the capacitance of a single conductor?

(g) Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (= 6).

Ans:

(a) When two charged spheres are brought close to each other, the charge distribution on them does not remain uniform. Therefore, the force between two conducting spheres is not exactly given by the given expression.

(b) Gauss’s law will not be true, if Coulomb’s law involved 1/r³ dependence, instead of 1/r² dependence.

(c) Yes, if a small test charge is released at rest at a point in an electrostatic field configuration, then it will move along the line of force passing through that point, only if the field lines are straight. If the field lines are not straight, the charge will not go along the line. This is because the field lines give the direction of acceleration.

(d) The direction of force due to field is towards the nucleus, and the electron does not move along the direction of this force. Therefore, whenever the electron completes an orbit, either circular or elliptical, the work done by the field of a nucleus is zero.

(e) No, electric potential is continuous across the surface of a charged conductor.

(f) The capacitance of a single conductor implies a parallel plate capacitor with one of its two plates at infinity.

(g) A water molecule has an unsymmetrical shape as compared to that of mica. Therefore, it has a permanent dipole moment. That is why; it has a greater dielectric constant than mica.

Note: Q&A containing MathML or Latex or Katex code cannot be rendered in pdf document.

FAQs: Class 12 Physics Chapter 2 – Electrostatic Potential and Capacitance

Q1. Is this chapter important for exams?
Yes, it is a high-weightage chapter for CBSE, JEE, and NEET.

Q2. Which topics are most important?
Electrostatic potential, capacitors, dielectrics, and energy stored in a capacitor.

Q3. Are numericals asked from this chapter?
Yes, capacitor combinations and energy-based numericals are common.

Q4. Are derivations important here?
Yes, derivations related to capacitance and energy of a capacitor are frequently asked.

Q5. How do NCERT Solutions help?
They provide NCERT-aligned, exam-ready explanations with solved numericals.