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

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

Vishal kumarUpdated on 20 Sep 2025, 07:53 PM IST

Did you realise that electricity can actually be stored and discharged when needed, as a power bank does for your mobile? This is achievable due to a device referred to as a capacitor, which holds the electrostatic charge and releases it in a burst-like manner, e.g., in a camera flash or some radio circuits. The concept of the electrical energy stored is a very interesting concept, which is related to potential energy, which you learned about in Class 11 Physics.

This Story also Contains

  1. Electrostatic Potential and Capacitance NCERT Solutions: Download PDF
  2. Electrostatic Potential and Capacitance NCERT Solutions: Exercises Solution
  3. Electrostatic Potential and Capacitance NCERT Solutions: Additional Questions
  4. Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance: Higher Order Thinking Skills (HOTS) Questions
  5. Approach to Solve Questions of Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance
  6. Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance: Important Topics
  7. Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance: Important Formulas
  8. What Extra Should Students Study Beyond NCERT for JEE/NEET?
  9. NCERT Solutions for Class 12 Physics Chapter-Wise
  10. Also Check NCERT Books and NCERT Syllabus here:
NCERT Solutions for Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance
Electric Potential and Capacitance

The NCERT Solutions for Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance are all the answers to each and every in-text and exercise question, step-by-step, in full detail, and without any errors. These NCERT solutions are carefully formulated by subject experts and simplify the process of learning by deconstructing the hard derivations and numerical problems into simple explanations. The key concepts addressed in this chapter are the electric potential, equipotential surfaces, as well as potential energy of a system of charges, capacitance of conductors, combination of capacitors and energy stored in a capacitor, and the use of dielectrics. These are not only essential to pass the CBSE Class 12 board exams but also to have a solid foundation for other competitive exams such as the JEE and NEET. By practising these NCERT Solutions for Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance regularly, students can enhance their conceptualisation in electrostatics, develop self-confidence in the ability to solve theoretical and numerical problems and learn the problem-solving that they need to achieve at the advanced physics level. The NCERT solutions are deemed as one of the most effective study resources in Class 12 Physics, whether one wants to study it on his/her own, complete an assignment, revise, or prepare it at the last moment.

Electrostatic Potential and Capacitance NCERT Solutions: Download PDF

Students who are about to undertake exams usually require fast, dependable and systematically arranged study content. NCERT Solutions of Chapter 2 -Electrostatic Potential and Capacitance of Class 12 Physics Chapter of the physics textbook are available in a step-by-step format in the PDF. By downloading this free PDF, offline access is easy, revision is easy, and examination is easy any time and anywhere.

Download PDF

Electrostatic Potential and Capacitance NCERT Solutions: Exercises Solution

Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance question answers of Exercises are straightforward solutions with step-by-step answers to every question in the textbook. These solutions are developed by professionals to enable students to learn how to solve problems and be more accurate when passing exams. These well-designed solutions are important to practice with to be well-structured and perform better on board and competitive exams.

2.1 Two charges 5×108C and 3×108C 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.

Answer:

Given two charge particles

q1=5108C

q2=3108C

The separation between two charged particles d=16cm=0.16m

Now, let's assume the point P between two charged particles where the electric potential is zero is x meter away from q1 and (9x) meter away from q2

So,

The potential at point P :

Vp=kq1x+kq20.16x=0

Vp=k5108x+k(3108)0.16x=0

k5108x=k(3108)0.16x

5(0.16x)=3x

x=0.1m=10cm

Hence the point between two charged particles where the electric potential is zero lies 10cm away from q1 and 6 cm away from q2

Now, Let's assume a point Q which is outside the line segment joining two charges and having zero electric potential. Let the point Q lie r meter away from q2 and (0.16+r) meter away from q1

So electric potential at point Q = 0

kq10.16+r+kq2r=0

k51080.16+r+k(3108)r=0

5r=3(0.16+r)

r=0.24m=24cm

Hence the second point where the electric potential is zero is 24cm away from q2 and 40cm away from q1

2.2 A regular hexagon of side 10 cm has a charge 5μC at each of its vertices. Calculate the potential at the centre of the hexagon.

Answer:

1643085531033

The electric potential at O due to one charge,

V1=q4πϵ0r

q = 5 × 10 -6 C

r = distance between charge and O = 10 cm = 0.1 m

Using the superposition principle, each charge at the corners contributes in the same direction to the total electric potential at point O.

V=6×q4πϵ0r

V=6×9×109Nm2C2×5×106C0.1m=2.7×106V

Therefore, the required potential at the centre is 2.7×106V

2.3 (a) Two charges 2μC and 2μC are placed at points A and B 6 cm apart. Identify an equipotential surface of the system.

Answer:

Given 2 charges with charges 2μC and 2μC .

An equipotential plane is a plane where the electric potential is the same at every point on the plane. Here if we see the plane which is perpendicular to line AB and passes through the midpoint of the line segment joining A and B, we see that at every point the electric potential is zero because the distance of all the points from two charged particles is the same. Since the magnitude of charges is the same, they cancel out the electric potential between them.

Hence required plane is a plane perpendicular to the line AB and passing through the midpoint of AB which is 3cm away from both charges.

2.3 (b) Two charges 2μC and 2μC are placed at points A and B, 6 cm apart. What is the direction of the electric field at every point on this surface?

Answer:

The direction of the electric field on this surface is normal to the plane and in the direction of the line joining A and B. Since both charges have the same magnitude and different signs, they cancel out the component of the electric field which is parallel to the surface.

2.4 (a) A spherical conductor of radius 12 cm has a charge of 1.6×107C distributed uniformly on its surface. What is the electric field inside the sphere?

Answer:

Since the charge is uniformly distributed and it always remains on the surface of the conductor, the electric field inside the sphere will be zero.

2.4 (b) A spherical conductor of radius 12 cm has a charge of 1.6×107C distributed uniformly on its surface. What is the electric field just outside the sphere?

Answer:

Given,

Charge on the conductor q=1.6107C

The radius of a spherical conductor R=12cm=0.12m

Now,

The electric field outside the spherical conductor is given by:

E=kqr2=14πϵqr2=91091.61070.122=105NC1

Hence electric field just outside is 105NC1 .

2.4 (c) A spherical conductor of radius 12 cm has a charge of 1.6×107C distributed uniformly on its surface. What is the electric field at a point 18 cm from the centre of the sphere?

Answer:

Given,

charge on the conductor q=1.6107C

The radius of the spherical conductor R=12cm=0.12m

Now,

The electric field at point 18cm away from the centre of the spherical conductor is given by:

E=kqr2=14πϵqr2=91091.61070.182=4.4104NC1

Hence electric field at the point 18cm away from the centre of the sphere is 4.4104NC1

2.5 A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF=1012F) . 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?

Answer:

As we know,

C=ϵrϵ0Ad

where A= area of the plate

ϵ0 = permittivity of the free space

d = distance between the plates.

Now, Given

The capacitance between plates initially

Cinitial=8pF=ϵAd

Now, capacitance when the distance is reduced by half and filled with the substance of dielectric 6

Cfinal=6ϵ0Ad/2=12ϵ0Ad=128pF=96pF

Hence new capacitance is 96pF.

2.6 (a) Three capacitors each of capacitance 9 pF are connected in series. What is the total capacitance of the combination?

Answer:

Given 3 capacitors of 9pF connected in series,

The equivalent capacitance when connected in series is given by

1Cequivalent=1C1+1C2+1C3

1Cequivalent=19+19+19=39=13

Cequivalent=3pF

Hence total capacitance of the combination is 3pF

2.6 (b) Three capacitors each of capacitance 9 pF are connected in series. What is the potential difference across each capacitor if the combination is connected to a 120 V supply?

Answer:

Given,

Supply Voltage V = 120 V

The potential difference across each capacitor will be one-third of the total voltage

Vc=V3=1203=40V

Hence potential difference across each capacitor is 40V.

2.7 (a) Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. What is the total capacitance of the combination?

Answer:

Given, 3 capacitors with C1=2pF,C2=3pFandC3=4pF are connected in series,

The equivalent capacitance when connected in parallel is given by

Cequivalant=C1+C2+C3

Cequivalant=2+3+4=9pF

Hence, the equivalent capacitance is 9pF.

2.7 (b) Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. Determine the charge on each capacitor if the combination is connected to a 100 V supply.

Answer:

Given, 3 capacitors connected in parallel with

C1=2pF

C2=3pF

C3=4pF

Supply voltage V=100V

Since they are connected in parallel, the voltage across each capacitor is 100V.

So, charge on 2pf capacitor :

Q1=C1V=21012100=21010C

Charge on 3pF capacitor:

Q2=C2V=31012100=31010C

Charge on 4pF capacitor:

Q3=C3V=41012100=41010C

Hence charges on capacitors are 200pC,300pC and 400pC respectively

2.8 In a parallel plate capacitor with air between the plates, each plate has an area of 6×103m2 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?

Answer:

Given,

Area of the capacitor plate A = 6×103m2

Distance between the plates d=3mm

Now,

The capacitance of the parallel plate capacitor is

C=ϵ0Ad

ϵ0 = permittivity of free space = 8.8541012N1m2C2

putting all known value we get,

C=8.854101261033103=17.711012F=17.71pF

Hence capacitance of the capacitor is 17.71pF.

Now,

Charge on the plate of the capacitor :

Q=CV=17.711012100=1.771109C

Hence charge on each plate of the capacitor is 1.771109C .

2.9 (a) 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,while the voltage supply remained connected.

Answer:

Given,

The dielectric constant of the inserted mica sheet = 6

The thickness of the sheet = 3mm

Supply voltage V=100V

Initial capacitance = Cinitial=1.7711011F

Final capacitance = KCinitial

Final capacitance =61.7711011F

Final capacitance =1061012F

Final charge on the capacitor = Qfinal=CfinalV
=1061012100
=1061010C

Hence on inserting the sheet charge on each plate changes to 1061010C .

2.9 (b) Explain what would happen if in the capacitor given, a 3 mm thick mica sheet (of dielectric constant = 6) were inserted between the plates, after the supply was disconnected.

Answer:

If a 3mm mica sheet is inserted between plates of the capacitor after disconnecting it from the power supply, the voltage across the capacitor will be changed. Since the charge on the capacitor can not go anywhere, if we change the capacitance (which we are doing by inserting mica sheet here), the voltage across the capacitor has to be adjusted accordingly.

As obtained from question number 8 charge on each plate of the capacitor is 1.771109C

Vfinal=QCfinal=1.771×109106×1012=16.7V

2.10 A 12pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor?

Answer:

As we know,

the electrostatic energy stored in the capacitor is

E=12CV2

Here,

C=12pF

V=50V

So,

E=12CV2=12121012502=1.5108J

Hence energy stored in the capacitor is 1.5108J

2.11 A 600pF capacitor is charged by a 200V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?

Answer:

Given

C=600pF

V=200V

Energy stored :

E=12CV2=126001012200200=1.2105J

Now, when it is disconnected and connected to another capacitor of capacitance 600pF

New capacitance

C=600600600+600=300pF

New electrostatic energy

E=12CV2=1230010122002=0.6105J

Hence loss in energy

EE=1.21050.6105J=0.6105J

Electrostatic Potential and Capacitance NCERT Solutions: Additional Questions

Electrostatic Potential and Capacitance class 12 question answers - Additional Questions will provide the students with additional practice on top of the textbook questions. These questions help in the enhancement of problem-solving skills, learning of tricky principles and organising learners to take tests at higher levels such as JEE and NEET. Being a great revision and practice guide, they include step-by-step proven solutions.

1. A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of 2×109C from a point P (0, 0, 3 cm) to a point Q (0, 4 cm, 0), via a point R (0, 6 cm, 9 cm).

Answer:

Given,

The initial distance between two charges

dinitial=3cm

The final distance between two charges

dfinal=4cm

Hence total work is done

W=q2(kq1dfinalkq1dinitial)=kq1q24πϵ0(1dfinal1dinitial)

W=91098103(2109)(10.0410.03)=1.27J

The path of the charge does not matter; only the initial and final positions matters.

2. A cube of side b has a charge q at each of its vertices. Determine the potential and electric field due to this charge array at the centre of the cube.

Answer:

As we know,

the distance between vertices and the centre of the cube

d=3b2

Where b is the side of the cube.

So potential at the centre of the cube:

P=8kqd=8kqb3/2=16kqb3

Hence electric potential at the centre will be

16kqb3=16q4πϵ0b3=4qπϵ0b3

The electric field will be zero at the centre due to symmetry i.e. every charge lying in the opposite vertices will cancel each other's field.

3. (a) Two tiny spheres carrying charges 1.5μC and 2.5μC are located 30 cm apart. Find the potential and electric field at the mid-point of the line joining the two charges

Answer:

As we know

outside the sphere, we can assume it like a point charge. so,

the electric potential at midpoint of the two-sphere

V=kq1d/2+kq2d/2

where q1 and q2 are charges and d is the distance between them

So,

V=k1.51060.15+k2.51060.15=2.4105V

The electric field

E=k1.51060.152k2.51060.152=4105V/m

3. (b) Two tiny spheres carrying charges 1.5μC and 2.5μC are located 30 cm apart. Find the potential and electric field at a point 10 cm from this midpoint in a plane normal to the line and passing through the mid-point.

Answer:

The distance of the point from both the charges :

d=0.12+0.152=0.18m

Hence,

Electric potential:

V=kq1d+kq2d=k0.18(1.5+2.5)106=2105V

Electric field due to q1

E1=kq1d2=k1.5μC0.182m2=0.416106V/m

Electric field due to q2

E2=kq2d2=k2.5μC0.182m2=0.69106V/m

Now,

Resultant Electric field :

E=E12+E22+2E1E2cosθ

Where θ is the angle between both electric field directions

Here,

cosθ2=0.100.18=59

θ2=56.25

θ=256.25=112.5

Hence

E=(0.416106)2+(0.69106)2+2(0.416106)(0.69106)cos112.5

E=6.6105V/m

4. (a) A spherical conducting shell of inner radius r 1 and outer radius r 2 has a charge Q.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?

Answer:

The charge placed on the centre is q, so -q will be the charge induced in the inner shell and + q will be induced in the outer shell

So,

charge density on the inner shell

σinner=q4πr12

charge Density on the outer shell

σouter=Q+q4πr22

4. (b) A spherical conducting shell of inner radius r 1 and outer radius r 2 has a charge Q. Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

Answer:

Yes, the electric field inside the cavity is zero even when the shape is irregular and not the sphere. Suppose a Gaussian surface inside the cavity, now since there is no charge inside it, the electric flux through it will be zero according to the guess law. Also, all of the charges will reside on the surface of the conductor so, net charge inside is zero. hence electric field inside cavity is zero.

5. (a) Show that the normal component of the electrostatic field has a discontinuity from one side of a charged surface to another given by (E1E2).n^=σϵ0 where n^ is a unit vector normal to the surface at a point and σ is the surface charge density at that point. Hence, show that just outside a conductor, the electric field is σn^ϵ0 [Hint: Use Gauss’s law]

Answer:

The electric field on one side of the surface with charge density σ

E1=σ2ϵ0n^

The electric field on another side of the surface with charge density σ

E2=σ2ϵ0n^

Now, resultant of both surfaces:

As E1 and E2 are opposite in direction. we have

E1E2=σ2ϵ0(σ2ϵ0)n^=σϵ0

There has to be a discontinuity at the sheet of the charge since both electric fields are in the opposite direction.

Now,

Since the electric field is zero inside the conductor,

the electric field just outside the conductor is

E=σϵ0n^

5. (b) Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another. [Hint: Use the fact that work done by electrostatic field on a closed loop is zero.]

Answer:

Let's assume a rectangular loop of length l and small width b.

Now,

Line integral along the loop :

E.dl=E1lE2l=0

This implies

E1cosθ1lE2cosθ2l=0

From here,

E1cosθ1=E2cosθ2

Since E1cosθ1 and E2cosθ2 are the tangential component of the electric field, the tangential component of the electric field is continuous across the surface

6. A long charged cylinder of linear charged density λ is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders?

Answer:

The charge density of the cylinder with length l and radius r = λ

The radius of another hollow cylinder with the same length = R

Now, let our gaussian surface be a cylinder with the same length and different radius r

the electric flux through Gaussian surface

E.ds=qϵ0

E.2πrl=λlϵ0

E=λ2πϵ0r

Hence electric field ar a distance r from the axis of the cylinder is

E=λ2πϵ0r

7. (a) In a hydrogen atom, the electron and proton are bound at a distance of about 0.53A˙ Estimate the potential energy of the system in eV, taking the zero of the potential energy at an infinite separation of the electron from proton

Answer:

As we know,

the distance between electron-proton of the hydrogen atom

d=0.531010m

The potential energy of the system = potential energy at infinity - potential energy at distance d

PE=0keed=9109(1.61019)20.531010=43.71019J

As we know,

1ev=1.61019J

PE=43.710191.61019=27.2eV

Hence potential energy of the system is -27.2eV.

7. (b) In a hydrogen atom, the electron and proton are bound at a distance of about 0.53A˙ 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)?

Answer:

The potential energy of the system is -27.2eV. (from the previous question)

Kinetic energy is half of the potential energy in magnitude. so kinetic energy = 27/2 = 13.6eV

so,

total energy = 13.6 - 27.2 = -13.6eV

Hence the minimum work required to free the electron is 13.6eV

7. (c) In a hydrogen atom, the electron and proton are bound at a distance of about 0.53 A˙. What are the answers to (a) and (b) above if the zero of potential energy is taken at 1.06 A˙ separation?

Answer:

When potential energy is zero at d 1.06 A˙ away,

The potential energy of the system =potential energy at d -potential energy at d

PE=kepd127.2=9109(1.61019)21.061010=13.6eV

Hence potential energy, in this case, would be -13.6eV

8. If one of the two electrons of a H 2 molecule is removed, we get a hydrogen molecular ion H2+ . In the ground state of an H2+ , the two protons are separated by roughly 1.5 A˙ , and the electron is roughly 1 A˙ from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy.

Answer:

Given,

Distance between proton 1 and 2

dp1p2=1.51010m

Distance between proton 1 and electron

dp1e=11010m

Distance between proton 2 and electron

dp2e=11010m

Now,

The potential energy of the system :

V=kp1edp1e+kp2edp2e+kp1p2dp1p2

Substituting the values, we get

V=9109101910191010[(16)2+(1.6)21.5(1.6)2]=19.2eV

9. 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.

Answer:

Since both spheres are connected through the wire, their potential will be the same

Let the electric field at A and B be EA and EB .

Now,

EAEB=QAQBb2a2

also

QAQB=CaVCBV

Also

CACB=ab

Therefore,

EAEB=ab2ba2=ba

Therefore the ratio of the electric field is b/a.

10. (a) Two charges –q and +q are located at points (0, 0, –a) and (0, 0, a), respectively. What is the electrostatic potential at the points (0, 0, z) and (x, y, 0) ?

Answer:

1)electric potential at point (0,0,z)

distance from q1

d1=02+02+(0az)2=a+z

distance from q2

d2=02+02+(az)2=az

Now,

Electric potential :

V=kq1a+z+kq2az=2kqaz2a2

2) Since the point,(x,y,0) lies in the normal to the axis of the dipole, the electric potential at this point is zero.

10. (b) Two charges –q and +q are located at points (0, 0, –a) and (0, 0, a), respectively. Obtain the dependence of potential on the distance r of a point from the origin when ra>>1

Answer:

Here, since distance r is much greater than half the distance between charges, the potential V at a distance r is inversely proportional to the square of the distance

V1r2

10. (c) Two charges –q and +q are located at points (0, 0, –a) and (0, 0, a), respectively 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?

Answer:

Since point (5,0,0) is equidistant from both charges, they both will cancel out each other's potential and hence the potential at this point is zero.

Similarly, point (–7,0,0) is also equidistant from both charges. and hence potential at this point is zero.

Since the potential at both points is zero, the work done in moving a charge from one point to another is zero. Work done is independent of the path.

11. Figure 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 ra>>1 , and contrast your results with that due to an electric dipole, and an electric monopole (i.e., a single charge).

1643085660448

Answer:

Here, as we can see

The electrostatic potential caused by the system of three charges at point P is given by

V=14πε0[qr+a2qr+qra]

V=14πε0[r(ra)2(r+a)(ra)+r(r+a)r(r+a)(ra)]=q4πϵ0[2a2r(r2a2)]

V=q4πϵ0[2a2r3(1a2r2)]

Since

ra>>1

V=2qa24πϵ0r3

From here, we conclude that

V1r3

Whereas we know that for a dipole,

V1r2

And for a monopole,

V1r

12. An electrical technician requires a capacitance of 2μF in a circuit across a potential difference of 1 kV. A large number of 1μF capacitors are available to him each of which can withstand a potential difference of not more than 400 V. Suggest a possible arrangement that requires the minimum number of capacitors

Answer:

Let's assume n capacitors connected in series and m numbers of such rows,

Now,

As given

The total voltage of the circuit = 1000V

and the total voltage a capacitor can withstand = 400

From here the total number of the capacitors in series

n=1000400=2.5

Since the number of capacitors can never be a fraction, we take n = 3.

Now,

Total capacitance required = 2μF

Number of rows we need

m=2n=23=6

Hence capacitors should be connected in 6 parallel rows, where each row contains 3 capacitors in series.

13. 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 realise from your answer why ordinary capacitors are in the range of μF or less. However, electrolytic capacitors do have a much larger capacitance (0.1 F) because of very minute separation between the conductors.]

Answer:

Given,

The capacitance of the parallel plate capacitor C=2F

Separation between plated d=0.5cm

Now, as we know

C=ϵ0Ad

A=Cdϵ0=251038.851012=1.13109m2

A=1.13103km2=1130km2

Hence, to get capacitance in farads, the area of the plate should be of the order of a kilometre, which is not good practice, and that is why ordinary capacitors are of the range μF

14. Obtain the equivalent capacitance of the network in Figure. For a 300 V supply, determine the charge and voltage across each capacitor.

1643085694762

Answer:

Given.

C1=100pF

C2=200pF

C3=200pF

C4=100pF

Now,

Let's first calculate the equivalent capacitance of C2andC3

C23=C2C3C2+C3=200200200+200=100pF

Now let's calculate the equivalent of C1andC23

C123=C1+C23=100+100=200pF

Now let's calculate the equivalent of C123andC4

Cequivalent=C123C4C123+C4=100200100+200=2003pF

Now,

The total charge on C4 capacitors:

Q4=CequivalentV=20031012300=2108C

So,

V4=Q4C4=21081001012=200V

The voltage across C1 is given by

V1=VV4=300200=100V

The charge on C1 is given by

Q1=C1V1=1001012100=108C

The potential difference across C2andC3 is

V2=V3=50V

Hence Charge on C2

Q2=C2V2=200101250=108C

And Charge on C3 :

Q3=C3V3=200101250=108C

15. (a) 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. How much electrostatic energy is stored by the capacitor?

Answer:

Here

The capacitance of the parallel plate capacitor :

C=ϵ0Ad

The electrostatic energy stored in the capacitor is given by :

E=12CV2=12ε0AdV2=1.885101290104400222.5103=2.55106J

Hence, the electrostatic energy stored by the capacitor is 2.55106J.

15. (b) 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. 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.

Answer:

The volume of the capacitor is:

V=Ad=9010425103=2.25104m3

Now,

Energy stored in the capacitor per unit volume :

u=EV=2.551062.55104=0.113perm3

Now, the relation between u and E.

u=EV=12CV2Ad=12(ϵ0Ad)V2Ad=12ϵ0E2

16. A 4 μF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 2 μF capacitors. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?

Answer:

Here,

The charge on the capacitance initially

Q=CV=4106200=8104C

Total electrostatic energy initially

Einitial=12CV2=124106(200)2=8102J

Now, when it is disconnected and connected to another capacitor

Total new capacitance = Cnew=4+2=6μF

Now, by conserving the charge on the capacitor:

VnewCnew=CinitialVinitial

Vnew6μF=4μF200

Vnew=4003V

Now,

New electrostatic energy :

Enew=12CnewVnew2=126106(4003)2=5.33102J

Therefore,

Lost in electrostatic energy

E=EinitialEnew=0.080.0533=0.0267J

17. Show that the force on each plate of a parallel plate capacitor has a magnitude equal to (12) QE, where Q is the charge on the capacitor, and E is the magnitude of electric field between the plates. Explain the origin of the factor (12)

Answer:

Let

The surface charge density of the capacitor = σ

Area of the plate = A

Now,

As we know,

Q=σAandE=σϵ0

When the separation is increased by Δx,

work done by external force= FΔx

Now,

Increase in potential energy :

ΔU=UAΔx

By the work-energy theorem,

FΔx=YAΔx

F=UA=12ϵ0E2A

putting the value of ϵ0

F=12σEE2A=12σAE=12QE

The origin of 1/2 lies in the fact that the field is zero inside the conductor and field just outside is E, hence it is the average value of E/2 that contributes to the force.

18. A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports figure. Show that the capacitance of a spherical capacitor is given by C=4πϵ0r1r2r1r2 where r1 and r2 are the radii of outer and inner spheres, respectively.

1643085726693

Answer:

Given

The radius of the outer shell = r1

The radius of the inner shell = r2

charge on the Inner surface of the outer shell = Q

Induced charge on the outer surface of the inner shell = Q

Now,

The potential difference between the two shells

V=Q4πϵ0r2Q4πϵ0r1

Now Capacitance is given by

C=Charge(Q)Potentialdifference(V)

C=QQ(r1r2)4πϵ0r1r2=4πϵ0r1r2r1r2

Hence proved.

19. (c) 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 μ C. The space between the concentric spheres is filled with a liquid of dielectric constant 32. Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller.

Answer:

The radius of the isolated sphere r=4.5102

Now, the Capacitance of a sphere:

Cnew=4πϵ0r=4π8.851012121012=1.331011F

On comparing it with the concentric sphere, it is evident that it has lesser capacitance. This is due to the fact that the concentric sphere is connected to the Earth.

Hence, the potential difference is less and the capacitance is more than the isolated sphere.

20. (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 Q1Q24πϵ0r2 , where r is the distance between their centres?

Answer:

The charge on the sphere is not exactly a point charge; we assume it when the distance between two bodies is large. When the two charged spheres are brought closer, the charge distribution on them will no longer remain uniform. Hence, it is not true that the electrostatic force between them is exactly given by Q1Q24πϵ0r2 .

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

Answer:

Since the solid angle is proportional to 1r2 and not proportional to 1r3 ,

The Gauss law, which is equivalent to Coulomb's law, will not hold true.

20. (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?

Answer:

When a small test charge is released at rest at a point in an electrostatic field configuration, it travels along the field line passing through that point only if the field lines are straight, because electric field lines give the direction of acceleration, not the velocity

20. (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?

Answer:

The initial and final positions will be the same for any orbit, whether it is circular or elliptical. Hence, work done will always be zero.

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

Answer:

Since the electric potential is not a vector quantity, unlike the electric field, it can never be discontinuous.

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

Answer:

There is no meaning in the capacitor with a single plate, factually. but we give it meaning by assuming the second plate at infinity. Hence capacitance of a single conductor is the amount of charge required to raise the potential of the conductor by one unit.

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

Answer:

Water has a much greater dielectric constant than mica because it possesses a permanent dipole moment and has an unsymmetrical shape.

21. A cylindrical capacitor has two co-axial cylinders of length 15 cm and radii 1.5 cm and 1.4 cm. The outer cylinder is earthed and the inner cylinder is given a charge of 3.5 μ C. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).

Answer:

Given

Length of cylinder l=15cm

inner radius a=1.4cm

outer radius b=1.5cm

Charge on the inner cylinder q=3.5μC

Now as we know,

The capacitance of this system is given by

C=2πϵ0l2.303log10(b/a)

C=2π8.8541012151022.303log10(1.5102/1.4102)=1.211010F

Now

Since the outer cylinder is earthed, the potential at the inner cylinder is equal to the potential difference between the two cylinders.

So

Potential of inner cylinder:

V=qC=3.51061.211010=2.89104V

22. A parallel plate capacitor is to be designed with a voltage rating 1 kV, using a material of dielectric constant 3 and dielectric strength about 107Vm1 . (Dielectric strength is the maximum electric field a material can tolerate without breakdown, i.e., without starting to conduct electricity through partial ionisation.) For safety, we should like the field never to exceed, say 10% of the dielectric strength. What minimum area of the plates is required to have a capacitance of 50 pF?

Answer:

Given

Voltage rating in designing a capacitor V=1kV=1000V

The dielectric constant of the material K=ϵr=3

Dielectric strength of material = 107V/m

Safety Condition:

E=10100107=106V/m

The capacitance of the plate C=50pF

Now, as we know,

E=Vd

d=VE=103106=103m

Now,

C=ε0εrAd

A=Cdϵ0ϵr=5010121038.8510123=1.98103m2

Hence the minimum required area is 1.98103m2

23. (a) Describe schematically the equipotential surfaces corresponding to a constant electric field in the z-direction

Answer:

When the electric field is in the z-direction is constant, the potential in a direction perpendicular to z-axis remains constant. In other words, every plane parallel to the x-y plane is an equipotential plane.

23. (b) Describe schematically the equipotential surfaces corresponding to a field that uniformly increases in magnitude but remains in a constant (say, z) direction

Answer:

The potential in a direction perpendicular to the direction of the field is always gonna be same irrespective of the magnitude of the electric field. Hence equipotential surface will be the plane, normal of which is the direction of the field.

23. (c) Describe schematically the equipotential surfaces corresponding to a single positive charge at the origin.

Answer:

For a single positive charge, the equipotential surface will be the sphere with centre at the position of the charge, which is the origin in this case.

23. (d) Describe schematically the equipotential surfaces corresponding to a uniform grid consisting of long equally spaced parallel charged wires in a plane.

Answer:

The equipotential surface near the grid is periodically varying, and after a long distance, it becomes parallel to the grid.

24. A small sphere of radius r1 and charge q1 is enclosed by a spherical shell of radius r2 and charge q2. Show that if q1 is positive, charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge q2 on the shell is.

Answer:

The potential difference between the inner sphere and shell;

V=14πϵ0q1r1

So, the potential difference is independent of q2 . And hence whenever q_{1} is positive, the charge will flow from the sphere to the shell

25. (a) The top of the atmosphere is at about 400 kV with respect to the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about 100 Vm1 . Why then do we not get an electric shock as we step out of our house into the open? (Assume the house to be a steel cage so there is no field inside!)

Answer:

The surface of the earth and our body are both good conductors. So our body and the ground both have the same equipotential surface, as we are connected to the ground. When we move outside the house, the equipotential surfaces in the air change so that our body and the ground are kept at the same potential. Therefore we do not get an electric shock.

25. (b) A man fixes outside his house one evening a two metre high insulating slab carrying on its top a large aluminium sheet of area 1m2. Will he get an electric shock if he touches the metal sheet next morning?

Answer:

Yes, the man will get an electric shock. The aluminium sheet is gradually charged up by discharging current from the atmosphere. Eventually, the voltage will increase up to a certain point depending on the capacitance of the capacitor formed by the aluminium sheet, the insulating slab and the ground. When the man touches that charged metal, he will get a shock.

25. (c) The discharging current in the atmosphere due to the small conductivity of air is known to be 1800 A on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words, what keeps the atmosphere charged?

Answer:

Thunderstorms and lightning across the globe keep the atmosphere charged by releasing light energy, heat energy, and sound energy in the atmosphere. In one way or another, the atmosphere is discharged through regions of ordinary weather. on an average, the two opposing currents are in equilibrium. Hence, the atmosphere perpetually remains charged.

25. (d) What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning? (Hint: The earth has an electric field of about 100 Vm1 at its surface in the downward direction, corresponding to a surface charge density = 109Cm2 . Due to the slight conductivity of the atmosphere up to about 50 km (beyond which it is good conductor), about + 1800 C is pumped every second into the earth as a whole. The earth, however, does not get discharged since thunderstorms and lightning occurring continually all over the globe pump an equal amount of negative charge on the earth.)

Answer:

Electrical energy, of the atmosphere, is dissipated as light energy, which comes from lightning, heat energy and sound energ,y which comes from the thunderstorm.

Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance: Higher Order Thinking Skills (HOTS) Questions

The NCERT Class 12 Physics Chapter 2- HOTS (Higher Order Thinking Skills) questions are designed to enhance the analytical and logical thinking ability. These difficult problems extend beyond what can be applied directly, and these problems push the students to think critically and transfer concepts to new situations. Their practice gives them confidence in taking competitive exams such as JEE and NEET, and also confidence that they have learned the basics of Physics.

Q1. The stored energy of a capacitor charged to 100 V, is 1 J. The capacitance of the capacitor is -

Answer:

The energy stored in a capacitor,

U=12CV2.

Rearrange the formula to solve for capacitance

C=2UV2.

On Substituting the values U=1J and V=100 V into the formula,
C=2×11002=210000=0.0002 F.


The capacitance of the capacitor is 2×104 F.

Q.2 A capacitor is filled by two dielectric materials equally in two configurations as shown in the figure. The dielectric constants of materials are K1=1.25 and K2=2.25 and the capacitances in two configurations are C1 and C2 respectively, find out the approximate value of C1C2 when expressed as an integer.

Answer:

The first arrangement is a parallel combination.

C1=K1ε0(A/2)d=12K1ε0Ad

and C2=12K2ε0Ad

C1=C1+C2=12(K1+K2)ε0Ad


The second arrangement is a series combination:

C1=K1ε0Ad/2=2K1ε0AdC2=K2ε0Ad/2=2K2ε0AdC2=C1C2C1+C2=K1K2K1+K22ε0AdC1C2=(K1+K2)24K1K2=4948


The approximate value of 4948 when expressed as an integer is 1.


Q.3 Two equal charges q are placed at a distance of 2a and a third charge -2q is placed at the midpoint. The potential energy of the system is -

Answer:


Potential energy -
U=14πϵ0q(2q)a+14πϵ0q(2q)a+14πϵ0qq2q=14πσ0q2a[22+12]U=14πϵ0q2a(72)=7q28πϵ0a

Q.4 Twenty-seven drops of water of the same size are equally and similarly changed. They are then united to form a bigger drop. By what factor will the electrical potential change?

A) 9 times

B) 27 times

C) 6 times

D) 3 times
Answer:

Let VB is the potential of a bigger drop and VS potential of a small drop.

use, VB=n2/3Vs(1)

but n=27. put in (1) we get-

VB=(27)2/3VsVB=(33)2/3Vs=32VsVB=9VS9 times


Hence, the answer is the option 1A

Q.5 Find the total charge (in μC) stored in the network of capacitors connected between A and B as shown in figure :

Answer:

The given circuit is a balanced bridge. Total capacitance

C=2×42+4+6×36+3=43+2=103μFQ=CV=103μF×3V=10μC

Hence, the answer is 10.

Approach to Solve Questions of Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance

Solving Physics questions effectively requires a structured method that balances conceptual clarity with logical problem-solving. By breaking down each problem into smaller steps and applying the right formulas at the right stage, students can avoid confusion and errors. Developing a systematic approach ensures accuracy, saves time in exams, and builds confidence in tackling both numerical and theoretical problems.

Electric Potential:

  • First, Learn how potential is created by a charge, a dipole or a group of charges.
JEE Main Highest Scoring Chapters & Topics
Just Study 40% Syllabus and Score upto 100%
Download EBook

Use Diagrams:

  • Equipotential lines and field lines help you "see" how charges and potentials are arranged.

Understand Capacitors:

  • Know how a capacitor stores charge and energy. Focus on parallel plate capacitors and what factor affects the capacitance of a capacitor.

Combination of Capacitors:

  • Practice the combination of capacitors in series and parallel it is similar to resistors, but with opposite rules.

Know Dielectrics:

  • See how inserting a material (dielectric) between plates changes the capacitor's ability to store charge.

Practice NCERT Questions:

  • Most exam questions come from the NCERT. Solve all examples and exercises to get exam-ready.

Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance: Important Topics

In order to study well before taking exams, students should make emphasis on the important concepts that have maximum weightage. Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance, contains a number of basic principles, which provide the foundation of not only advanced physics, but also competitive examinations. The following is a list of the strategic aspects that the students will use to revise in a systematic way and enhance the preparation.

Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance: Important Formulas

Mastering the formulas of Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance is essential for solving numerical problems quickly and accurately in exams. These formulas not only simplify complex derivations but also help in applying concepts directly to JEE, NEET, and board-level questions. A quick revision of these key formulas ensures better problem-solving speed and boosts confidence during exam preparation.

1. Electrostatic Potential (V):V=Wq, where W is work done to bring charge q from infinity to a point.
2. Potential Due to a Point Charge: V=14πε0q.
3. Potential Due to a Dipole: V=14πε0pcosθr2, where p=qd is dipole moment.
4. Relation Between Field and Potential: E=dVdr.
5. Capacitance of a Capacitor: C=QV.
6. Parallel Plate Capacitor: C=ε0Ad.
7. Effect of Dielectric: C=kC, where k is the dielectric constant.
8. Combination of Capacitors:
Series: 1Ceq =1C1+1C2+
Parallel: Ceq =C1+C2+

What Extra Should Students Study Beyond NCERT for JEE/NEET?

Although NCERT offers the fundamental basis of the knowledge of Electrostatic Potential and Capacitance, competitive examinations such as JEE and NEET require in-depth problem-solving and conceptual implementation. To fill this gap, students need to read more complicated problem sets, mathematical applications with unusual twists, and different forms of theory. The table below indicates the disparity between the preparation in NCERT and the extra preparation needed in JEE/NEET.

NCERT Solutions for Class 12 Physics Chapter-Wise

The availability of the Chapter-by-Chapter solutions to Class 12 Physics in the NCERT makes the process of preparing the exams more efficient and formal. All in-text and exercise questions are answered step-by-step, in detail and on each link, allowing students to update on the essential concepts in a short time. The solutions are developed in line with the recent CBSE syllabus and are useful in board tests, competitive tests such as JEE and NEET and also in self study and practice of homework.

Frequently Asked Questions (FAQs)

Q: What is the significance of electric potential energy in electrostatics?
A:

Electric potential energy represents the stored energy due to the positions of charges in an electric field. It determines the work required to assemble a system of charges and plays a crucial role in electrostatic interactions.

Q: What are the practical applications of capacitors in daily life?
A:

Capacitors are widely used in electronic circuits for energy storage, power conditioning, signal filtering voltage regulation and in memory devices. They are essential components in devices like radios, televisions, electric motors, and even flash cameras.

Q: What is the importance of the Class 12 Physics unit Electrostatics for CBSE board exam?
A:

The unit Electrostatics have the first two chapters of Class 12 Physics. A total of 6 to 8 marks questions can be expected from the chapter for CBSE board exam. A good score can be obtained in the CBSE board exam by following NCERT syllabus and problems. For extra questions related to the chapter refer NCERT exemplar questions and the CBSE previous year board papers.

Q: What is the weightage of the chapter Electrostatic Potential and Capacitance for NEET exams?
A:

The Class 12 NCERT chapter Electrostatic Potential and Capacitance is an important chapter for NEET exams. Combining the chapter 1 and 2 of class 12 NCERT Physics a total of 8 to 10% questions can be expected for NEET.

Q: How many questions are asked from the chapter Electrostatic Potential and Capacitance for JEE main?
A:

A total of 2 or 3 questions can be expected from the unit Electrostatics. From the chapter Electrostatic Potential and Capacitance 1 or 2 questions can be expected or the questions may be using the combinations of concepts in the Class 12 Physics chapter 1 and 2

Articles
|
Upcoming School Exams
Ongoing Dates
UP Board 12th Others

10 Aug'25 - 27 Sep'25 (Online)

Ongoing Dates
UP Board 10th Others

10 Aug'25 - 27 Sep'25 (Online)

Certifications By Top Providers
Explore Top Universities Across Globe

Questions related to CBSE Class 12th

On Question asked by student community

Have a question related to CBSE Class 12th ?

Yes, you can switch from Science in Karnataka State Board to Commerce in CBSE for 12th. You will need a Transfer Certificate from your current school and meet the CBSE school’s admission requirements. Since you haven’t studied Commerce subjects like Accountancy, Economics, and Business Studies, you may need to catch up before or during 12th. Not all CBSE schools accept direct admission to 12th from another board, so some may ask you to join Class 11 first. Make sure to check the school’s rules and plan your subject preparation.



Hello

For the 12th CBSE Hindi Medium board exam, important questions usually come from core chapters like “Madhushala”, “Jhansi ki Rani”, and “Bharat ki Khoj”.
Questions often include essay writing, letter writing, and comprehension passages. Grammar topics like Tenses, Voice Change, and Direct-Indirect Speech are frequently asked.
Students should practice poetry questions on themes and meanings. Important questions also cover summary writing and translation from Hindi to English or vice versa.
Previous years’ question papers help identify commonly asked questions.
Focus on writing practice to improve handwriting and presentation. Time management during exams is key to answering all questions effectively.

Hello,

If you want to improve the Class 12 PCM results, you can appear in the improvement exam. This exam will help you to retake one or more subjects to achieve a better score. You should check the official website for details and the deadline of this exam.

I hope it will clear your query!!

For the 2025-2026 academic session, the CBSE plans to conduct board exams from 17 February 2026 to 20 May 2026.

You can download it in pdf form from below link

CBSE DATE SHEET 2026

all the best for your exam!!

Hii neeraj!

You can check CBSE class 12th registration number in:

  • Your class 12th board exam admit card. Please do check admit card for registration number, it must be there.
  • You can also check the registration number in your class 12th marksheet in case you have got it.
  • Alternatively you can also visit your school and ask for the same in the administration office they may tell you the registration number.

Hope it helps!