Physics · Textbook solutions

Electric Charges and Fields

Every solved example, exercise, and miscellaneous question, in the order the textbook teaches them. Plus every board question asked from this chapter. · 35 questions

Worked Examples

12 q

Solved Examples

Worked · 12

Eg 1.1 $10^{9}$
Eg 1.2 $How much positive and negative charge is there in a cup of water?$
Eg 1.3 $1\,\text{Å}$
Eg 1.4 $10\,\text{cm}$
Eg 1.5 $q_1$
Eg 1.6 $q$
Eg 1.7 $1.5\,\text{cm}$
Eg 1.8 $q_1$
Eg 1.9 $\pm 10\,\mu\text{C}$
Eg 1.10 $E_x = \alpha x^{1/2}$
Eg 1.11 $x$
Eg 1.12 $Ze$

Exercises

23 q

Ex 1.1 $2 \times 10^{-7}\,\text{C}$
Ex 1.2 $0.4\,\mu\text{C}$
Ex 1.3 $ke^{2}/G\,m_{e}m_{p}$
Ex 1.4 $(a) Explain the meaning of the statement 'electric charge of a body is quantised'. (b) Why can one ignore quantisation of electric charge when dealing with macroscopic i.e., large scale charges?$
Ex 1.5 $When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.$
Ex 1.6 $q_{A} = 2\,\mu\text{C}$
Ex 1.7 $(a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not? (b) Explain why two field lines never cross each other at any point?$
Ex 1.8 $q_{A} = 3\,\mu\text{C}$
Ex 1.9 $q_{A} = 2.5 \times 10^{-7}\,\text{C}$
Ex 1.10 $4 \times 10^{-9}\,\text{C m}$
Ex 1.11 $3 \times 10^{-7}\,\text{C}$
Ex 1.12 $50\,\text{cm}$
Ex 1.13 $Figure 1.30 shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?$
Ex 1.14 $\mathbf{E} = 3 \times 10^{3}\,\hat{\mathbf{i}}\,\text{N/C}$
Ex 1.15 $20\,\text{cm}$
Ex 1.16 $8.0 \times 10^{3}\,\text{N m}^{2}/\text{C}$
Ex 1.17 $+10\,\mu\text{C}$
Ex 1.18 $2.0\,\mu\text{C}$
Ex 1.19 $-1.0 \times 10^{3}\,\text{N m}^{2}/\text{C}$
Ex 1.20 $10\,\text{cm}$
Ex 1.21 $2.4\,\text{m}$
Ex 1.22 $9 \times 10^{4}\,\text{N/C}$
Ex 1.23 $17.0 \times 10^{-22}\,\text{C}/\text{m}^{2}$

What the board has asked from this chapter

Questions per paper · 21 papers · 2023 to 2026

Bars average the full papers of each year. 30 further questions come from set variants and are listed below.

2026

17 q

1 $-2q$
Tap an option to check your answer.
Coulomb's Law and Forces Between Multiple Charges
1 $\vec{E} = E_0 \hat{i}$
Tap an option to check your answer.
Electric Field and Field Lines
4 $\vec{P} = 2qa\,\hat{i}$
Tap an option to check your answer.
Electric Dipole and Dipole in a Uniform Field
5 $\vec{P} = (2{\cdot}54 \times 10^{-28}\ \mathrm{C.m})\,(2{\cdot}00\hat{i} + 3{\cdot}00\hat{j})$
Tap an option to check your answer.
Electric Dipole and Dipole in a Uniform Field
6 $-\mathrm{Q}$
Tap an option to check your answer.
Electric Field and Field Lines
7 $v_0\,\hat{i}$
Tap an option to check your answer.
Electric Field and Field Lines
9 $The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be :$
Tap an option to check your answer.
Electric Field and Field Lines
17 $+1\ \mu\mathrm{C}$
Electric Dipole and Dipole in a Uniform Field
22 (a) $\sigma$
Applications of Gauss's Law
24 $3 \times 10^7$
Electric Field and Field Lines
25 $q_1 = 2{\cdot}5 \times 10^{-7}$
Electric Dipole and Dipole in a Uniform Field
The electric potential (V) and electric field (E) are closely related concepts in electrostatics. The electric field is a vector quantity that represents the force per unit charge at a given point in space, whereas electric potential is a scalar quantity that represents the potential energy per unit charge at a given point in space. Electric field and electric potential are related by the equations $\mathrm{E_r} = \dfrac{-dV}{dr}$ and $\vec{\mathrm{E}} = \mathrm{E_r}\hat{r}$ , i.e., electric field is the negative gradient of the electric potential. This means that electric field points in the direction of decreasing potential and its magnitude is the rate of change of potential with distance. The electric field is the force that drives a unit charge to move from higher potential region to lower potential region and electric potential difference between the two points determines the work done in moving a unit charge from one point to the other point. A pair of square conducting plates having sides of length $0{\cdot}05$ m are arranged parallel to each other in x-y plane. They are $0{\cdot}01$ m apart along z-axis and are connected to a 200 V power supply as shown in the figure. An electron enters with a speed of $3 \times 10^7\ \mathrm{ms^{-1}}$ horizontally and symmetrically in the space between the two plates. Neglect the effect of gravity on the electron.
29 (ii) $\vec{a}$
Tap an option to check your answer.
Electric Field and Field Lines
The electric potential (V) and electric field (E) are closely related concepts in electrostatics. The electric field is a vector quantity that represents the force per unit charge at a given point in space, whereas electric potential is a scalar quantity that represents the potential energy per unit charge at a given point in space. Electric field and electric potential are related by the equations $\mathrm{E_r} = \dfrac{-dV}{dr}$ and $\vec{\mathrm{E}} = \mathrm{E_r}\hat{r}$ , i.e., electric field is the negative gradient of the electric potential. This means that electric field points in the direction of decreasing potential and its magnitude is the rate of change of potential with distance. The electric field is the force that drives a unit charge to move from higher potential region to lower potential region and electric potential difference between the two points determines the work done in moving a unit charge from one point to the other point. A pair of square conducting plates having sides of length $0{\cdot}05$ m are arranged parallel to each other in x-y plane. They are $0{\cdot}01$ m apart along z-axis and are connected to a 200 V power supply as shown in the figure. An electron enters with a speed of $3 \times 10^7\ \mathrm{ms^{-1}}$ horizontally and symmetrically in the space between the two plates. Neglect the effect of gravity on the electron.
29 (iii) (a) $Time interval during which an electron moves through the region between the plates is :$
Tap an option to check your answer.
Electric Field and Field Lines
The electric potential (V) and electric field (E) are closely related concepts in electrostatics. The electric field is a vector quantity that represents the force per unit charge at a given point in space, whereas electric potential is a scalar quantity that represents the potential energy per unit charge at a given point in space. Electric field and electric potential are related by the equations $\mathrm{E_r} = \dfrac{-dV}{dr}$ and $\vec{\mathrm{E}} = \mathrm{E_r}\hat{r}$ , i.e., electric field is the negative gradient of the electric potential. This means that electric field points in the direction of decreasing potential and its magnitude is the rate of change of potential with distance. The electric field is the force that drives a unit charge to move from higher potential region to lower potential region and electric potential difference between the two points determines the work done in moving a unit charge from one point to the other point. A pair of square conducting plates having sides of length $0{\cdot}05$ m are arranged parallel to each other in x-y plane. They are $0{\cdot}01$ m apart along z-axis and are connected to a 200 V power supply as shown in the figure. An electron enters with a speed of $3 \times 10^7\ \mathrm{ms^{-1}}$ horizontally and symmetrically in the space between the two plates. Neglect the effect of gravity on the electron.
29 (iii) (b) $The vertical displacement of the electron which travels through the region between the plates is :$
Tap an option to check your answer.
Electric Field and Field Lines
The electric potential (V) and electric field (E) are closely related concepts in electrostatics. The electric field is a vector quantity that represents the force per unit charge at a given point in space, whereas electric potential is a scalar quantity that represents the potential energy per unit charge at a given point in space. Electric field and electric potential are related by the equations $\mathrm{E_r} = \dfrac{-dV}{dr}$ and $\vec{\mathrm{E}} = \mathrm{E_r}\hat{r}$ , i.e., electric field is the negative gradient of the electric potential. This means that electric field points in the direction of decreasing potential and its magnitude is the rate of change of potential with distance. The electric field is the force that drives a unit charge to move from higher potential region to lower potential region and electric potential difference between the two points determines the work done in moving a unit charge from one point to the other point. A pair of square conducting plates having sides of length $0{\cdot}05$ m are arranged parallel to each other in x-y plane. They are $0{\cdot}01$ m apart along z-axis and are connected to a 200 V power supply as shown in the figure. An electron enters with a speed of $3 \times 10^7\ \mathrm{ms^{-1}}$ horizontally and symmetrically in the space between the two plates. Neglect the effect of gravity on the electron.
29 (iv) $Which one of the following is the path traced by the electron in between the two plates ?$
Tap an option to check your answer.
Electric Field and Field Lines
31 (a) $\vec{E}$
Electric Dipole and Dipole in a Uniform Field
31 (b) $-\lambda$
Applications of Gauss's Law

2025

18 q

1 $\vec{E}$
Tap an option to check your answer.
Coulomb's Law and Forces Between Multiple Charges
1 $A charge Q is fixed in position. Another charge q is brought near charge Q and released from rest. Which of the following graphs is the correct representation of the acceleration of the charge q as a function of its distance r from charge Q ?$
Tap an option to check your answer.
Coulomb's Law and Forces Between Multiple Charges
1 $1{\cdot}0 \times 10^{-12}$
Tap an option to check your answer.
Electric Dipole and Dipole in a Uniform Field
1 $\frac{1}{r^2}$
Tap an option to check your answer.
Coulomb's Law and Forces Between Multiple Charges
1 $8{\cdot}0 \times 10^{-12}$
Tap an option to check your answer.
Electric Charge and its Basic Properties
1 $-q$
Tap an option to check your answer.
Electric Field and Field Lines
1 $D_1$
Tap an option to check your answer.
Electric Dipole and Dipole in a Uniform Field
3 $v\,\hat{i}$
Tap an option to check your answer.
Electric Field and Field Lines
8 $Which one of the following statements is correct ? Electric field due to static charges is$
Tap an option to check your answer.
Electric Field and Field Lines
23 $\vec{E}$
Electric Flux and Gauss's Law
28 (b) $\lambda$
Applications of Gauss's Law
31 (a) $0{\cdot}2$
Electric Dipole and Dipole in a Uniform Field
31 (b) $y > r$
Applications of Gauss's Law
31 (b) $d\vec{S}$
Electric Flux and Gauss's Law
31 (b) $+6q$
Applications of Gauss's Law
32 (a) $0{\cdot}2$
Electric Dipole and Dipole in a Uniform Field
32 (b) $y > r$
Applications of Gauss's Law
33 (b) $\vec{E}$
Electric Dipole and Dipole in a Uniform Field

2024

18 q

1 $m_P$
Tap an option to check your answer.
Electric Field and Field Lines
1 $\left(\dfrac{1}{r^2}\right)$
Tap an option to check your answer.
Coulomb's Law and Forces Between Multiple Charges
1 $\lambda$
Tap an option to check your answer.
Electric Field and Field Lines
1 $\vec{p}$
Tap an option to check your answer.
Electric Dipole and Dipole in a Uniform Field
2 $\lambda$
Tap an option to check your answer.
Applications of Gauss's Law
2 $+ q$
Tap an option to check your answer.
Coulomb's Law and Forces Between Multiple Charges
2 $B_1$
Tap an option to check your answer.
Electric Charge and its Basic Properties
2 $\sigma$
Tap an option to check your answer.
Applications of Gauss's Law
2 $(1/r^2)$
Tap an option to check your answer.
Coulomb's Law and Forces Between Multiple Charges
For Questions 13 to 16, two statements are given – one labelled Assertion (A) and other labelled Reason (R). Select the correct answer to these questions from the options as given below. (A) If both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A). (B) If both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A). (C) If Assertion (A) is true but Reason (R) is false. (D) If both Assertion (A) and Reason (R) are false.
13 $Assertion (A) : Equal amount of positive and negative charges are distributed uniformly on two halves of a thin circular ring as shown in figure. The resultant electric field at the centre O of the ring is along OC. Reason (R) : It is so because the net potential at O is not zero.$
Tap an option to check your answer.
Electric Field and Field Lines
17 (a) $1\ \mu\mathrm{C}$
Coulomb's Law and Forces Between Multiple Charges
17 (b) $Three point charges, 1 pC each, are kept at the vertices of an equilateral triangle of side 10 cm. Find the net electric field at the centroid of triangle.$
Electric Field and Field Lines
22 $0{\cdot}1$
Electric Flux and Gauss's Law
23 $\vec{E} = \left(100\ \frac{\mathrm{N}}{\mathrm{C}}\right)\hat{i}$
Electric Flux and Gauss's Law
31 (b) $\sigma$
Applications of Gauss's Law
31 (b) $\vec{E}$
Applications of Gauss's Law
31 (b) $(\sigma)$
Applications of Gauss's Law
32 (b) $\vec{E}$
Applications of Gauss's Law

2023

28 q

1 $30^\circ$
Tap an option to check your answer.
Electric Dipole and Dipole in a Uniform Field
1 $q_1$
Tap an option to check your answer.
Coulomb's Law and Forces Between Multiple Charges
1 $A charge Q is placed at the centre of a cube. The electric flux through one if its face is$
Tap an option to check your answer.
Electric Flux and Gauss's Law
1 $\vec{F}$
Tap an option to check your answer.
Electric Dipole and Dipole in a Uniform Field
1 $(1{\cdot}6 \times 10^{-16}\ \mathrm{N})\ \hat{i}$
Tap an option to check your answer.
Electric Field and Field Lines
1 $16\,\dfrac{\mathrm{N}}{\mathrm{C}}$
Tap an option to check your answer.
Electric Field and Field Lines
2 $Which one of the following is not a scalar quantity ?$
Tap an option to check your answer.
Electric Field and Field Lines
4 $-q$
Tap an option to check your answer.
Coulomb's Law and Forces Between Multiple Charges
4 $18 \times 10^{4}\ \mathrm{NC^{-1}}$
Tap an option to check your answer.
Applications of Gauss's Law
5 $\vec{\mathrm{E}}$
Tap an option to check your answer.
Electric Field and Field Lines
6 $\lambda$
Tap an option to check your answer.
Applications of Gauss's Law
7 $2 \times 10^{-8}$
Tap an option to check your answer.
Electric Dipole and Dipole in a Uniform Field
9 $\mathrm{q}_0$
Tap an option to check your answer.
Coulomb's Law and Forces Between Multiple Charges
19 $Two identical dipoles are arranged in x-y plane as shown in the figure. Find the magnitude and the direction of net electric field at the origin O.$
Electric Dipole and Dipole in a Uniform Field
21 $Use Gauss's law to obtain the expression for electric field due to a thin infinitely long straight uniformly charged wire.$
Applications of Gauss's Law
22 $\vec{p}$
Electric Dipole and Dipole in a Uniform Field
22 $Depict the orientation of an electric dipole in (a) stable and (b) unstable equilibrium in an external uniform electric field. Write the potential energy of the dipole in each case.$
Electric Dipole and Dipole in a Uniform Field
24 $Use Gauss's law to obtain the expression for electric field due to a uniformly charged infinite plane thin sheet.$
Applications of Gauss's Law
31 (a) $\hat{i}$
Coulomb's Law and Forces Between Multiple Charges
31 (a) $\lambda$
Applications of Gauss's Law
31 (a) $\vec{\mathrm{E}} = (\mathrm{A}x + \mathrm{B})\ \hat{i}\ \dfrac{\mathrm{N}}{\mathrm{C}}$
Applications of Gauss's Law
31 (b) $\sqrt{2}$
Electric Dipole and Dipole in a Uniform Field
A beam of electrons moving horizontally with a velocity of $3 \times 10^{7}$ m/s enters a region between two plates as shown in the figure. A suitable potential difference is applied across the plates such that the electron beam just strikes the edge of the lower plate.
34 (a) $How long does an electron take to strike the edge ?$
Electric Field and Field Lines
Electrostatics deals with the study of forces, fields and potentials arising from static charges. Force and electric field, due to a point charge is basically determined by Coulomb's law. For symmetric charge configurations, Gauss's law, which is also based on Coulomb's law, helps us to find the electric field. A charge/a system of charges like a dipole experience a force/torque in an electric field. Work is required to be done to provide a specific orientation to a dipole with respect to an electric field.
34 (a) $|\vec{\mathrm{E}}|$
Applications of Gauss's Law
A beam of electrons moving horizontally with a velocity of $3 \times 10^{7}$ m/s enters a region between two plates as shown in the figure. A suitable potential difference is applied across the plates such that the electron beam just strikes the edge of the lower plate.
34 (b) $What is the shape of the path followed by the electron and why ?$
Electric Field and Field Lines
A beam of electrons moving horizontally with a velocity of $3 \times 10^{7}$ m/s enters a region between two plates as shown in the figure. A suitable potential difference is applied across the plates such that the electron beam just strikes the edge of the lower plate.
34 (c) $Find the potential difference applied.$
Electric Field and Field Lines
Electrostatics deals with the study of forces, fields and potentials arising from static charges. Force and electric field, due to a point charge is basically determined by Coulomb's law. For symmetric charge configurations, Gauss's law, which is also based on Coulomb's law, helps us to find the electric field. A charge/a system of charges like a dipole experience a force/torque in an electric field. Work is required to be done to provide a specific orientation to a dipole with respect to an electric field.
34 (c) $6 \times 10^{-7}$
Electric Dipole and Dipole in a Uniform Field
Electrostatics deals with the study of forces, fields and potentials arising from static charges. Force and electric field, due to a point charge is basically determined by Coulomb's law. For symmetric charge configurations, Gauss's law, which is also based on Coulomb's law, helps us to find the electric field. A charge/a system of charges like a dipole experience a force/torque in an electric field. Work is required to be done to provide a specific orientation to a dipole with respect to an electric field.
34 (c) OR $\vec{p}$
Electric Dipole and Dipole in a Uniform Field

The 10 board questions to practise first

The questions the board asked again come first, most asked first. Each one says how often and when.

Question 1
Asked 2 times: 2023, 2026
22 (a) $\sigma$
Question 2
Asked 2 times: 2024*, 2026 (* = numbers or wording changed that year)
17 $+1\ \mu\mathrm{C}$
Question 3
Asked 2 times: 2024, 2025
1 $\frac{1}{r^2}$
Tap an option to check your answer.
Question 4
Asked 2 times: 2023, 2024
2 $\lambda$
Tap an option to check your answer.
Question 5
This type asked 3 times: 2023, 2024, 2026. This one: 2024
32 (b) $\vec{E}$
Question 6
This type asked 3 times: 2023, 2025, 2026. This one: 2026
31 (a) $\vec{E}$
Question 7
This type asked 3 times: 2023, 2024, 2026. This one: 2026
5 $\vec{P} = (2{\cdot}54 \times 10^{-28}\ \mathrm{C.m})\,(2{\cdot}00\hat{i} + 3{\cdot}00\hat{j})$
Tap an option to check your answer.
Question 8
This type asked 3 times: 2024, 2025, 2026. This one: 2026
6 $-\mathrm{Q}$
Tap an option to check your answer.
Question 9
This type asked 2 times: 2025, 2026. This one: 2026
31 (b) $-\lambda$
Question 10
This type asked 2 times: 2023, 2026. This one: 2026
24 $3 \times 10^7$

Worked Examples

Solved Examples

Exercises

What the board has asked from this chapter

2026

2025

2024

2023

The 10 board questions to practise first

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10