Physics · Class 12 Science
Ch 1Electric Charges and Fields — Class 12 Physics, concept-first.
Most of us have felt a small shock or heard a crackle while taking off a synthetic sweater or clothing, especially in dry weather — have you ever wondered why? A related, larger-scale example is the lightning we see in the sky during a thunderstorm.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Photoelectric Effect
Imagine you're throwing tennis balls at a wall covered in loose pebbles. If you throw hard enough, a pebble might get knocked off.
Most relevant Q&A
- If $10^9$ electrons move out of a body to another body every second, how much time is required to get a total charge of $1\,\text{C}$ on the…Free
- How much positive and negative charge is there in a cup of water? (Assume the mass of one cup of water to be $250\,\text{g}$.)Preview
- (a) Explain the meaning of the statement 'electric charge of a body is quantised'. (b) Why can one ignore quantisation of electric charge wh…Preview
- A polythene piece rubbed with wool is found to have a negative charge of $3 \times 10^{-7}\,\text{C}$. (a) Estimate the number of electrons…Preview
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
Most of us have felt a small shock or heard a crackle while taking off a synthetic sweater or clothing, especially in dry weather — have you ever wondered why? A related, larger-scale example is the l…
Electric Charge
Electric charge is an intrinsic property of matter, just like mass. It is the source of the electric force.
Conductors and Insulators
Materials are classified based on how easily they allow electric charges to move through them.
Basic Properties of Electric Charge
Electric charge is a scalar quantity. The total charge of a system is the algebraic sum of all the individual charges present.
Additivity of Charges
Charge is a scalar quantity — it has magnitude but no direction, just like mass. However, unlike mass (which is always positive), charge can be positive or negative.
Charge Is Conserved
When two bodies are charged by rubbing, electrons are transferred from one body to the other. No new charge is created, and no existing charge is destroyed — only the carriers of charge (electrons) mo…
Quantisation of Charge
All observable electric charge in nature is quantised. This means charge cannot have any arbitrary value; it exists only in discrete, indivisible packets.
+−Worked Examplesi2 questions
- Example 1.1If $10^9$ electrons move out of a body to another body every second, how much time is required to get a total charge of $1\,\text{C}$ on the…Free
- Example 1.2How much positive and negative charge is there in a cup of water? (Assume the mass of one cup of water to be $250\,\text{g}$.)Preview
Coulomb's Law
Coulomb’s law is a quantitative statement that gives the electrostatic force between two point charges.
+−Worked Examplesi2 questions
- Example 1.3Coulomb's law for electrostatic force between two point charges and Newton's law for gravitational force between two stationary point masses…Free
- Example 1.4A charged metallic sphere A is suspended by a nylon thread. Another charged metallic sphere B held by an insulating handle is brought close…Preview
Forces Between Multiple Charges
Coulomb’s law tells us the force between two isolated charges. But what happens when a charge is surrounded by many others? The answer comes from the principle of superposition, which is experimentall…
+−Worked Examplesi2 questions
- Example 1.5Consider three charges $q_1$, $q_2$, $q_3$ each equal to $q$ at the vertices of an equilateral triangle of side $l$. What is the force on a…Free
- Example 1.6Consider the charges $q$, $q$, and $-q$ placed at the vertices of an equilateral triangle. What is the force on each charge?  creates an electric field in all of the space around it.
Electric Field Due to a System of Charges
The electric field due to a single point charge is defined as the force per unit positive test charge.
Physical Significance of Electric Field
In electrostatics, you can always find the force on a charge directly using Coulomb’s law and the superposition principle.
+−Worked Examplesi2 questions
- Example 1.7An electron falls through a distance of $1.5\,\text{cm}$ in a uniform electric field of magnitude $2.0 \times 10^{4}\,\text{N C}^{-1}$ [Fig.…Free
- Example 1.8Two point charges $q_1$ and $q_2$, of magnitude $+10^{-8}\,\text{C}$ and $-10^{-8}\,\text{C}$, respectively, are placed $0.1\,\text{m}$ apar…Preview
Electric Field Lines
The electric field is a vector — it has both magnitude and direction at every point. Drawing an arrow at every point in space is impractical.
Electric Flux
Electric flux is a concept borrowed from fluid flow. In a fluid, the flux measures how much fluid flows through a given area per unit time.
Electric Dipole
An electric dipole is formed by two equal and opposite point charges, and , separated by a fixed distance.
The Field of an Electric Dipole
An electric dipole consists of two equal and opposite charges, and , separated by a small distance . The electric field at any point in space is found by applying Coulomb’s law for each charge and the…
Physical Significance of Dipoles
Most molecules have their positive and negative charge centres at the same point, so their net dipole moment is zero. Examples include and .
Dipole in a Uniform External Field
A permanent dipole (dipole moment exists even without an external field) placed in a uniform external electric field experiences zero net force but a non-zero torque.
Continuous Charge Distribution
Discrete point charges () are mathematically simple, but real objects (like a charged metal sphere or a wire) contain an enormous number of microscopic charges.
Gauss's Law
Gauss's Law is a fundamental principle of electrostatics. It connects the total electric flux through any closed surface to the total electric charge trapped inside that surface.
+−Worked Examplesi2 questions
- Example 1.10The electric field components in Fig. 1.24 are $E_x = \alpha x^{1/2}$, $E_y = E_z = 0$, in which $\alpha = 800\,\text{N/C m}^{1/2}$. Calcula…Free
- Example 1.11An electric field is uniform, and in the positive $x$ direction for positive $x$, and uniform with the same magnitude but in the negative $x…Preview
Applications of Gauss's Law
The electric field due to a general charge distribution is given by the superposition integral (summing contributions from each charge element).
Field Due to an Infinitely Long Straight Uniformly Charged Wire
The wire is infinitely long and has a uniform linear charge density (charge per unit length). This infinite length creates a perfect symmetry: the wire is an axis of symmetry.
Field Due to a Uniformly Charged Infinite Plane Sheet
An infinite plane sheet with uniform surface charge density creates an electric field that is constant in magnitude and perpendicular to the sheet.
Field Due to a Uniformly Charged Thin Spherical Shell
The electric field of a uniformly charged thin spherical shell is a classic application of Gauss’s law.
Summary
- Coulomb’s Law: Force between two point charges and separated by distance in vacuum is , where . Force is along the line joining charges, attractive for opposite signs, repulsive for like signs.
Points to Ponder
1. Why protons stay together in the nucleus despite repelling each other is explained by the strong nuclear force, a third fundamental force.
Exercises
+−Show 23 questionsHide questions23 questions
- 1.1What is the force between two small charged spheres having charges of $2 \times 10^{-7}\,\text{C}$ and $3 \times 10^{-7}\,\text{C}$ placed $…Free
- 1.2The electrostatic force on a small sphere of charge $0.4\,\mu\text{C}$ due to another small sphere of charge $-0.8\,\mu\text{C}$ in air is $…Free
- 1.3Check that the ratio $k e^2 / G m_e m_p$ is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What…Free
- 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 wh…Preview
- 1.5When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Expl…Preview
- 1.6Four point charges $q_A = 2\,\mu\text{C}$, $q_B = -5\,\mu\text{C}$, $q_C = 2\,\mu\text{C}$, and $q_D = -5\,\mu\text{C}$ are located at the c…Preview
- 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 l…Preview
- 1.8Two point charges $q_A = 3\,\mu\text{C}$ and $q_B = -3\,\mu\text{C}$ are located $20\,\text{cm}$ apart in vacuum. (a) What is the electric f…Preview
- 1.9A system has two charges $q_A = 2.5 \times 10^{-7}\,\text{C}$ and $q_B = -2.5 \times 10^{-7}\,\text{C}$ located at points A: $(0, 0, -15\,\t…Preview
- 1.10An electric dipole with dipole moment $4 \times 10^{-9}\,\text{C m}$ is aligned at $30^\circ$ with the direction of a uniform electric field…Preview
- 1.11A polythene piece rubbed with wool is found to have a negative charge of $3 \times 10^{-7}\,\text{C}$. (a) Estimate the number of electrons…Preview
- 1.12(a) Two insulated charged copper spheres A and B have their centres separated by a distance of $50\,\text{cm}$. What is the mutual force of…Preview
- 1.13Figure 1.30 shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle ha…Preview
- 1.14Consider a uniform electric field $\mathbf{E} = 3 \times 10^{3}\,\hat{\mathbf{i}}\ \text{N/C}$. (a) What is the flux of this field through a…Preview
- 1.15What is the net flux of the uniform electric field of Exercise 1.14 through a cube of side $20\,\text{cm}$ oriented so that its faces are pa…Preview
- 1.16Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box i…Preview
- 1.17A point charge $+10\,\mu\text{C}$ is a distance $5\,\text{cm}$ directly above the centre of a square of side $10\,\text{cm}$, as shown in Fi…Preview
- 1.18A point charge of $2.0\,\mu\text{C}$ is at the centre of a cubic Gaussian surface $9.0\,\text{cm}$ on edge. What is the net electric flux th…Preview
- 1.19A point charge causes an electric flux of $-1.0 \times 10^{3}\,\text{N m}^2/\text{C}$ to pass through a spherical Gaussian surface of $10.0\…Preview
- 1.20A conducting sphere of radius $10\,\text{cm}$ has an unknown charge. If the electric field $20\,\text{cm}$ from the centre of the sphere is…Preview
- 1.21A uniformly charged conducting sphere of $2.4\,\text{m}$ diameter has a surface charge density of $80.0\,\mu\text{C/m}^2$. (a) Find the char…Preview
- 1.22An infinite line charge produces a field of $9 \times 10^{4}\,\text{N/C}$ at a distance of $2\,\text{cm}$. Calculate the linear charge densi…Preview
- 1.23Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposit…Preview
NCERT Exemplar
Higher-order thinking problems from the NCERT Exemplar.
+−Show 31 questionsHide questions31 questions
- Q1Two positive charges $q_2$ and $q_3$ are fixed on the $y$-axis (one on the $+y$ side, one on the $-y$ side, symmetric about the origin O). A…Free
- Q2A positive point charge $+q$ is brought near an isolated (uncharged) conducting sphere. Four candidate electric-field-line patterns are prop…Free
- Q3Four different closed surfaces, of different shapes and different sizes, are considered. Each one of the four surfaces encloses one and the…Free
- Q4Five point charges $q_1$, $q_2$, $q_3$, $q_4$ and $q_5$ are fixed at their positions in a plane. A closed Gaussian surface $S$ is drawn so t…Preview
- Q5An electric dipole is placed in a non-uniform electric field. The field lines all point in the same general direction (to the right, the $+x…Preview
- Q6A point charge $+q$ is placed at a distance $d$ from an isolated conducting plane. The field at a point $P$ on the other side of the plane i…Preview
- Q7A hemisphere is uniformly charged positively. The electric field at a point on a diameter away from the centre is directed (a) perpendicular…Preview
- Q8If $\oint_S \vec{E}\cdot d\vec{S} = 0$ over a surface, then (a) the electric field inside the surface and on it is zero. (b) the electric fi…Preview
- Q9The electric field at a point is (a) always continuous. (b) continuous if there is no charge at that point. (c) discontinuous only if there…Preview
- Q10If there were only one type of charge in the universe, then (a) $\oint_S \vec{E}\cdot d\vec{S} \neq 0$ on any surface. (b) $\oint_S \vec{E}\…Preview
- Q11Consider a region inside which there are various types of charges but the total charge is zero. At points outside the region, (a) the electr…Preview
- Q12Point charges are arranged along a straight horizontal line: a charge $Q$, a charge $5Q$ located a distance $R$ to the left of $Q$, and a ch…Preview
- Q13A positive charge $Q$ is distributed uniformly around a circular ring of radius $R$ lying in a plane. A small point test charge $q$ is place…Preview
- Q14An arbitrary surface encloses a dipole. What is the electric flux through this surface?Preview
- Q15A metallic spherical shell has an inner radius $R_1$ and outer radius $R_2$. A charge $Q$ is placed at the centre of the spherical cavity. W…Preview
- Q16The dimensions of an atom are of the order of an Angstrom. Thus there must be large electric fields between the protons and electrons. Why,…Preview
- Q17If the total charge enclosed by a surface is zero, does it imply that the electric field everywhere on the surface is zero? Conversely, if t…Preview
- Q18A hollow cylinder carries a uniform positive charge spread over its curved outer surface (both circular ends are open). The curved wall is u…Preview
- Q19A cube has side length $a$. A point charge $q$ is placed, in four separate cases, at the following positions relative to the cube: (a) at po…Preview
- Q20A paisa coin is made up of Al-Mg alloy and weighs $0.75\text{ g}$. It has a square shape and its diagonal measures $17\text{ mm}$. It is ele…Preview
- Q21Consider a coin of Question 1.20. It is electrically neutral and contains equal amounts of positive and negative charge of magnitude $34.8\t…Preview
- Q22A cubic unit cell of cesium chloride (CsCl) has cesium atoms situated at the eight corners of a cube of side $0.40\text{ nm}$, and a chlorin…Preview
- Q23Two charges $q$ and $-3q$ are placed fixed on $x$-axis separated by distance $d$. Where should a third charge $2q$ be placed such that it wi…Preview
- Q24The electric field lines around three point charges A, B and C are shown. Around charge A (on the left) field lines emerge and curve outward…Preview
- Q25Five equal point charges, each of magnitude $q$, are placed at the five corners A, B, C, D, E of a regular pentagon of side $a$. O is the ce…Preview
- Q26In 1959 Lyttleton and Bondi suggested that the expansion of the Universe could be explained if matter carried a net charge. Suppose that the…Preview
- Q27Consider a sphere of radius $R$ with charge density distributed as $\rho(r) = kr$ for $r \leq R$ and $\rho(r) = 0$ for $r > R$. (a) Find the…Preview
- Q28Two fixed, identical conducting plates $\alpha$ and $\beta$, each of surface area $S$, are held parallel to each other. Plate $\alpha$ (on t…Preview
- Q29There is another useful system of units, besides the SI/mks A system, called the cgs (centimeter-gram-second) system. In this system Coulomb…Preview
- Q30Two point charges, each equal to $-q$, are held fixed on a straight line, separated by a distance $2d$ (so each is a distance $d$ from the m…Preview
- Q31Total charge $-Q$ is uniformly spread along the length of a ring of radius $R$. A small test charge $+q$ of mass $m$ is kept at the centre o…Preview
CBSE Sample Papers
Questions from official CBSE sample papers.