JEE Advanced 2026 Paper 2 — Full Mock Test (54 Questions, 180 Marks)
Mathematics · Physics · Chemistry
This MCQ module is based on: Charges Coulombs Law
TOPIC 1 OF 38
Charges Coulombs Law
🎓 Class 12
Physics
CBSE
Theory
Ch 1 – Electric Charges and Fields
⏱ ~14 min
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Charges Coulombs Law
1.1 Introduction — The World of Static Electricity
If you comb your dry hair briskly and bring the comb near small bits of paper, the paper jumps up and clings to the comb. On a winter night, removing a woollen sweater often produces tiny crackling sparks. The blinding flash of lightning during a thunderstorm is the same phenomenon on a colossal scale. These observations reveal the existence of a fundamental property of matter called electric charge.
The branch of physics that studies charges at rest and the forces/fields they produce is called electrostatics. In this chapter, we explore charges, Coulomb's law, electric fields, dipoles and the elegant Gauss's law — the foundations on which modern electrical technology is built.
What you will learn in Part 1: The nature of charge, conductors and insulators, charging by induction, the three basic laws of charge (additivity, conservation, quantisation) and Coulomb's law with its vector form and superposition principle.
1.2 Electric Charge — A Brief History
Around 600 BC, the Greek philosopher Thales of Miletus noticed that a piece of amber, when rubbed with fur, could attract bits of straw. The Greek word for amber is elektron — the root of "electricity". Centuries later, Benjamin Franklin (1750) recognised that rubbed objects carry two opposite kinds of electricity, which he named positive and negative.
- Glass rod rubbed with silk becomes positively charged.
- Plastic rod (or ebonite) rubbed with wool becomes negatively charged.
- Like charges repel; unlike charges attract.
1.3 Conductors and Insulators
Materials are classified by how easily charges can move through them.
| Type | Property | Examples |
|---|---|---|
| Conductors | Contain many "free" electrons that drift under an applied field. | Metals (Cu, Ag, Al), graphite, human body, earth, electrolytic solutions. |
| Insulators | Electrons are tightly bound; charge stays wherever it is placed. | Glass, dry wood, rubber, plastic, porcelain, mica. |
When a charged body is connected to the earth through a conductor, the excess charge flows to the vast reservoir of the earth and the body becomes neutral. This process is called earthing or grounding, and it is the reason household electrical appliances have a green-wire earth pin — it protects the user from shock if the insulation fails.
1.4 Charging by Induction
A body can be charged without any direct contact with a charged object. This technique uses a conductor and temporary earthing. Consider a metal sphere on an insulating stand being charged by a negatively-charged plastic rod:
1Bring the rod close (no touch).
Free electrons in the sphere are repelled to the far side, leaving the near side with induced positive charge.
2Connect the far side to earth.
The repelled electrons escape through the earthing wire, since earth provides an essentially infinite "sink".
3Remove the earthing wire (rod still near).
The sphere is now left with a net positive charge, still attracted to the rod.
4Remove the rod.
The positive charge redistributes uniformly over the sphere's surface.
5Result.
The sphere is permanently charged with sign opposite to that of the rod, and the rod is unchanged.
1.5 Basic Properties of Electric Charge
(a) Additivity
Total charge on a body is the algebraic sum of all individual charges. If charges \(q_1 = +5\,\mu\text{C}\), \(q_2 = -3\,\mu\text{C}\), \(q_3 = +2\,\mu\text{C}\) exist on a system:
\[Q_{\text{total}} = q_1 + q_2 + q_3 = (+5) + (-3) + (+2) = +4\,\mu\text{C}\]
(b) Conservation of Charge
The net charge of an isolated system never changes. Charges may be transferred from one body to another, or pairs of equal and opposite charges may be created/destroyed together (pair production, pair annihilation), but the algebraic sum stays constant.
(c) Quantisation of Charge
Millikan's 1909 oil-drop experiment revealed that charge comes only in integer multiples of a basic quantum \(e\):
\[q = n\,e, \qquad n = 0,\pm 1,\pm 2,\ldots,\qquad e = 1.602 \times 10^{-19}\,\text{C}\]
You can never have a body with charge 1.5e or 2.3e; only whole-number multiples. At macroscopic scales (e.g. \(1\,\mu\text{C} \approx 6.25 \times 10^{12}e\)), quantisation is invisible and charge looks continuous.
1.6 Coulomb's Law
In 1785, the French physicist Charles Augustin de Coulomb measured the force between two point charges using his torsion balance and announced the inverse-square law bearing his name.
Coulomb's Law (scalar form): The magnitude of the electrostatic force between two point charges \(q_1\) and \(q_2\) separated by distance \(r\) in vacuum is
\[F = k\,\frac{|q_1 q_2|}{r^2}, \qquad k = \frac{1}{4\pi\varepsilon_0} \approx 9 \times 10^9\,\text{N m}^2/\text{C}^2\]
where \(\varepsilon_0 = 8.854 \times 10^{-12}\) C\(^2\)/(N·m\(^2\)) is the permittivity of free space.
Vector Form
Let \(\hat r_{12}\) be the unit vector directed from charge 1 toward charge 2, and \(\vec F_{21}\) the force exerted by charge 1 on charge 2. Then:
\[\vec F_{21} = \frac{1}{4\pi\varepsilon_0}\,\frac{q_1 q_2}{r^2}\,\hat r_{12}\]
If \(q_1 q_2 > 0\), \(\vec F_{21}\) points along \(\hat r_{12}\) (repulsion). If \(q_1 q_2 < 0\), it points opposite to \(\hat r_{12}\) (attraction). By Newton's third law, \(\vec F_{12} = -\vec F_{21}\).
Superposition Principle
When many point charges act on a single charge, the total force is the vector sum of the pair-wise forces:
\[\vec F_1 = \vec F_{12} + \vec F_{13} + \cdots + \vec F_{1N} = \sum_{i\ne 1}\frac{1}{4\pi\varepsilon_0}\frac{q_1 q_i}{r_{1i}^2}\hat r_{i1}\]
Each pair interacts independently — the presence of a third charge does not alter the Coulomb force between the first two.
Effect of a Medium
If the space between the charges is filled by an insulating medium (dielectric) of dielectric constant \(K\) (also called relative permittivity \(\varepsilon_r\)), the force is reduced:
\[F_{\text{medium}} = \frac{F_{\text{vacuum}}}{K}\]
For example, water has \(K \approx 80\), so Coulomb forces inside water are 80 times weaker than in vacuum.
Worked Examples — Coulomb's Law
Example 1: Force between two point charges
Two point charges \(q_1 = 2\,\mu\text{C}\) and \(q_2 = 3\,\mu\text{C}\) are placed 10 cm apart in vacuum. Find the magnitude of the force between them.
Given \(q_1 = 2\times 10^{-6}\) C, \(q_2 = 3\times 10^{-6}\) C, \(r = 0.10\) m.
\[F = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^2} = 9\times 10^9 \times \frac{(2\times 10^{-6})(3\times 10^{-6})}{(0.10)^2}\]
\[F = 9\times 10^9 \times \frac{6\times 10^{-12}}{10^{-2}} = 9\times 10^9 \times 6\times 10^{-10} = \boxed{5.4\,\text{N (repulsive)}}\]
Example 2: Electrostatic vs Gravitational force (H atom)
In a hydrogen atom, the electron and proton are separated by \(5.3\times 10^{-11}\) m. Compare the electrostatic force with the gravitational force between them.
\[F_e = \frac{ke^2}{r^2} = \frac{(9\times 10^9)(1.6\times 10^{-19})^2}{(5.3\times 10^{-11})^2} = 8.2\times 10^{-8}\,\text{N}\]
\[F_g = \frac{G m_e m_p}{r^2} = \frac{(6.67\times 10^{-11})(9.1\times 10^{-31})(1.67\times 10^{-27})}{(5.3\times 10^{-11})^2} = 3.6\times 10^{-47}\,\text{N}\]
\[\frac{F_e}{F_g} \approx \boxed{2.3\times 10^{39}}\]
The electrostatic force utterly dominates at atomic scales.
Example 3: Three charges at the corners of an equilateral triangle
Equal positive charges \(q = 1\,\mu\text{C}\) are placed at each vertex of an equilateral triangle of side \(a = 10\) cm. Find the net force on one of them.
Each of the other two charges exerts a force of magnitude
\[F = \frac{kq^2}{a^2} = \frac{(9\times 10^9)(10^{-6})^2}{(0.10)^2} = 0.9\,\text{N}\]
The two forces make an angle of 60° with each other. Using the parallelogram law:
\[F_{\text{net}} = \sqrt{F^2 + F^2 + 2F^2\cos 60°} = F\sqrt{3} = 0.9\sqrt{3}\,\text{N}\]
\[\boxed{F_{\text{net}} \approx 1.56\,\text{N, directed outward along the perpendicular bisector}}\]
Example 4: Charge at the centre of a square
Four equal point charges \(+Q\) are placed at the corners of a square of side \(a\). A charge \(+q\) sits at the centre. What is the net force on \(+q\)?
By symmetry, the four forces on \(+q\) from the four corner charges are equal in magnitude and point outward along the four diagonals. Forces from diagonally-opposite corners are equal and opposite and therefore cancel exactly.
\[\boxed{\vec F_{\text{net}} = 0}\]
The centre is a position of equilibrium (though unstable).
Example 5: Force in a dielectric medium
Two charges of \(+4\,\mu\)C each are placed 20 cm apart in kerosene (K = 2). Find the force between them.
In vacuum: \(F_{\text{vac}} = \dfrac{(9\times 10^9)(4\times 10^{-6})^2}{(0.20)^2} = 3.6\,\text{N}.\)
\[F_{\text{med}} = \frac{F_{\text{vac}}}{K} = \frac{3.6}{2} = \boxed{1.8\,\text{N}}\]
Example 6: Number of electrons transferred
A comb rubbed against dry hair acquires a charge of \(-4.8\times 10^{-9}\) C. How many electrons did it gain?
\[n = \frac{|q|}{e} = \frac{4.8\times 10^{-9}}{1.6\times 10^{-19}} = \boxed{3\times 10^{10}\ \text{electrons}}\]
Activity — Induced Attraction on Paper BitsL3 Apply
Predict: When a charged comb is brought close to small uncharged paper pieces, why do the paper bits — despite being neutral — get attracted and stick to the comb?
- Tear a tissue paper into tiny bits (about 3–4 mm).
- Comb your dry hair briskly several times.
- Slowly bring the comb close to the paper bits without touching them.
- Observe which side of the paper bits jumps up first.
Observation: The paper bits leap up and stick to the comb.
Explanation: Although the paper is neutral, the charged comb polarises it by induction. Electrons in the paper bits shift slightly (being dielectric, they cannot flow freely but they polarise), producing a small induced charge opposite to the comb on the near side. Since the near-side attraction is stronger than the far-side repulsion (\(F \propto 1/r^2\)), a net attractive force pulls the paper toward the comb.
Explanation: Although the paper is neutral, the charged comb polarises it by induction. Electrons in the paper bits shift slightly (being dielectric, they cannot flow freely but they polarise), producing a small induced charge opposite to the comb on the near side. Since the near-side attraction is stronger than the far-side repulsion (\(F \propto 1/r^2\)), a net attractive force pulls the paper toward the comb.
Interactive: Coulomb Force Calculator L3 Apply
Enter two charges (in μC) and their separation (in cm). Find the magnitude of the Coulomb force in vacuum.
Competency-Based Questions
A physics teacher demonstrates electrostatics with two identical metallic spheres A and B, initially neutral, mounted on insulating stands. She charges sphere A to \(+8\,\mu\text{C}\) and then allows it to touch sphere B momentarily before separating them by 20 cm.
Q1. L1 Remember What is the charge on each sphere after they are separated?
Answer: B. Identical spheres in contact share charge equally, so each gets \(+4\,\mu\text{C}\).
Q2. L3 Apply Calculate the Coulomb force between A and B after separation. (3 marks)
\(F = \dfrac{k q_A q_B}{r^2} = \dfrac{9\times 10^9 (4\times 10^{-6})^2}{(0.20)^2} = \boxed{3.6\,\text{N (repulsive)}}\).
Q3. L3 Apply Two point charges \(+5\,\mu\text{C}\) and \(-5\,\mu\text{C}\) are 30 cm apart. Find the force between them. (2 marks)
\(F = \dfrac{9\times 10^9 (5\times 10^{-6})(5\times 10^{-6})}{(0.30)^2} = \boxed{2.5\,\text{N (attractive)}}\).
Q4. L4 Analyse A charge of \(+0.1\,\mu\text{C}\) experiences a force of 0.9 N due to a second charge 10 cm away. Find the second charge. (3 marks)
\(q_2 = \dfrac{F r^2}{k q_1} = \dfrac{0.9 \times (0.10)^2}{9\times 10^9 \times 10^{-7}} = \boxed{10^{-5}\,\text{C} = 10\,\mu\text{C}}\).
Q5. L2 Understand Can a charge be 3.2 × 10⁻¹⁹ C? Justify using quantisation. (2 marks)
\(n = 3.2 \times 10^{-19} / 1.6 \times 10^{-19} = 2\), an integer. So yes — it corresponds to \(2e\), a valid charge.
Assertion-Reason Questions
Assertion (A): Charge of a body is always an integral multiple of \(e\).
Reason (R): Free charges occur only as integer multiples of the elementary charge.
Answer: A. Quantisation is a universal law; R is exactly the statement underpinning A.
Assertion (A): Coulomb's force is a central force.
Reason (R): The force always acts along the line joining the two point charges.
Answer: A. A central force is defined as one directed along the line joining the two interacting bodies — exactly the content of R.
Assertion (A): Force between two charges in water is less than in vacuum.
Reason (R): The dielectric constant of water is much greater than 1.
Answer: A. \(F_{\text{med}} = F_{\text{vac}}/K\); with \(K_{\text{water}} \approx 80\), force drops by a factor of 80.
Frequently Asked Questions - Charges Coulombs Law
What is the main concept covered in Charges Coulombs Law?
In NCERT Class 12 Physics Chapter 1 (Electric Charges and Fields), "Charges Coulombs Law" covers the core principles and equations students need for board exam success. The MyAiSchool lesson explains the topic with definitions, derivations, worked examples, and interactive simulations. Key formulas and dimensional analysis are included to build conceptual depth and problem-solving skills aligned with the CBSE 2025-26 syllabus.
How is Charges Coulombs Law useful in real-life applications?
Real-life applications of "Charges Coulombs Law" from NCERT Class 12 Physics Chapter 1 include electronics, communication systems, medical imaging, solar energy, semiconductor devices, and modern technology. The MyAiSchool lesson links every concept to a tangible example so students see physics as a problem-solving framework for the physical world, not as abstract formulas.
What are the key formulas in Charges Coulombs Law?
Key formulas in "Charges Coulombs Law" (NCERT Class 12 Physics Chapter 1 Electric Charges and Fields) are derived step-by-step in the MyAiSchool lesson. Students should memorize the final formula AND understand its derivation for full board marks. Each formula is listed with its dimensional formula, SI unit, applicability range, and common pitfalls. The Summary section at the end of each part includes a quick-reference formula card.
How does this part connect to other parts of Chapter 1?
NCERT Class 12 Physics Chapter 1 (Electric Charges and Fields) is structured so each part builds on the previous one. "Charges Coulombs Law" connects directly to neighbouring parts via shared definitions, units, and methodology. The MyAiSchool lesson cross-references related concepts with internal links so students can navigate the whole chapter as one connected story rather than disconnected fragments.
What types of CBSE board questions come from Charges Coulombs Law?
CBSE board questions from "Charges Coulombs Law" typically include: (1) 1-mark MCQs on definitions and formulas, (2) 2-mark short-answer derivations or applications, (3) 3-mark numerical problems with units, (4) 5-mark long-answer derivations followed by application. The MyAiSchool lesson tags each Competency-Based Question (CBQ) with Bloom level (L1-L6) so students know how to study for each weight.
How can students use the interactive simulation effectively?
The interactive simulation in the "Charges Coulombs Law" lesson allows students to adjust input parameters (sliders or selectors) and see physical quantities update in real time. To use it effectively: (1) try extreme values to understand limiting cases, (2) compare with the analytical formula, (3) check unit consistency, (4) test special configurations from worked examples. The simulation reinforces conceptual intuition that pure formula manipulation cannot.
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