Two similarly charged bodies are kept 5 cm apart in air. If the second body is shifted away from the first by another 5 cm, their force of repulsion will be

1. Fundamentals of Electric Charges (basic)

Welcome to your first step in mastering Electricity and Magnetism! To understand how the lights turn on or how your phone charges, we must start with the most basic building block: the Electric Charge. Charge is an intrinsic property of matter, much like mass. There are two types: positive and negative. The golden rule here is simple—like charges repel each other, while unlike charges attract.

The interaction between these charges is governed by Coulomb’s Law. It tells us that the force between two charges depends on two things: the magnitude of the charges and the distance between them. Specifically, this force follows an inverse-square law. This means that the force is not just inversely proportional to the distance, but to the square of the distance. For example, if you double the distance between two charged spheres, the force between them doesn't just drop to half; it drops to one-fourth (1/2²) of its original strength. This principle is vital for understanding how charges behave in both a vacuum and within conductors.

When these charges are set in motion, we call it Electric Current. Think of current (I) as the rate at which charge (Q) flows through a specific point over time (t), expressed as I = Q/t Science, Class X (NCERT 2025 ed.), Electricity, p.172. Interestingly, due to historical conventions, we consider the direction of electric current to be from the positive terminal to the negative terminal. However, in reality, the electrons (which carry a negative charge) flow in the opposite direction—from negative to positive Science, Class X (NCERT 2025 ed.), Electricity, p.171.

Finally, charges don't just move on their own. They require "electric pressure," known as Potential Difference. Imagine a water tank: water only flows through a pipe if there is a difference in height or pressure between the two ends. Similarly, electrons in a wire only flow if there is a potential difference along the conductor, usually provided by a battery or cell Science, Class X (NCERT 2025 ed.), Electricity, p.173.

Sources: Science, Class X (NCERT 2025 ed.), Electricity, p.171; Science, Class X (NCERT 2025 ed.), Electricity, p.172; Science, Class X (NCERT 2025 ed.), Electricity, p.173

2. Materials: Conductors, Insulators, and Dielectrics (basic)

To understand electricity, we must first look at the materials through which it travels. At the atomic level, the behavior of electrons determines how a substance reacts to an electric field. In conductors, the outermost electrons are loosely bound to their atoms, allowing them to drift freely throughout the material. These "free electrons" are the charge carriers that make electrical current possible. Metals like silver, copper, and gold are the most efficient conductors, though copper is the standard for household wiring because it is both effective and affordable Science-Class VII, Electricity: Circuits and their Components, p.36.

On the opposite end of the spectrum are insulators. In these materials, electrons are tightly bound to their parent atoms and cannot move easily. Because they offer extremely high resistance to the flow of charge, they are essential for safety. We use insulators like rubber, plastic, and ceramics to coat wires and switches, ensuring that the electricity stays within the circuit and doesn't pass through our bodies, which would cause an electric shock Science-Class VII, Electricity: Circuits and their Components, p.36. Interestingly, even among conductors, some are better than others; a component that offers significant resistance is called a resistor, while insulators offer the highest resistance of all Science, class X, Electricity, p.177.

Feature	Conductors	Insulators
Electron Mobility	High (Free electrons)	Low (Bound electrons)
Electrical Resistance	Low	Very High
Common Examples	Copper, Aluminium, Iron	Rubber, Glass, Plastic
Primary Use	Carrying current	Safety and protection

Finally, we have dielectrics, which are a specific type of insulator. While they don't conduct electricity, they can be "polarized." This means that when exposed to an electric field, the charges within their atoms shift slightly, creating internal tension. This property is what allows static charges to build up on surfaces, such as when clouds rub together during a storm to create lightning Science, Class VIII, Pressure, Winds, Storms, and Cyclones, p.91. In our homes, we distinguish these paths through color-coded insulation: the live wire (usually red), the neutral wire (black), and the earth wire (green) for safety Science, class X, Magnetic Effects of Electric Current, p.206.

Sources: Science-Class VII . NCERT(Revised ed 2025), Electricity: Circuits and their Components, p.36; Science , class X (NCERT 2025 ed.), Electricity, p.177; Science , class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.206; Science ,Class VIII . NCERT(Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p.91

3. The Four Fundamental Forces of Nature (intermediate)

To understand the universe, we must look at the interactions that govern everything from the smallest subatomic particles to the largest galaxies. These are known as the Four Fundamental Forces of Nature. Every physical phenomenon you see—be it a compass needle moving, a ball falling, or the sun shining—is a result of one of these four interactions.

1. Gravitational Force: This is the force of attraction between any two objects with mass. As you may know from your geography studies, it is the force that makes objects fall toward the Earth and keeps planets in their orbits Science Class VIII, Exploring Forces, p.72. Interestingly, while gravity is the most obvious force in our daily lives, it is actually the weakest of the four. However, it has an infinite range, meaning it acts across the entire universe.
2. Electromagnetic Force: This is the star of our current learning path. It acts between electrically charged particles. Unlike gravity, which only attracts, the electromagnetic force can be either attractive (opposite charges) or repulsive (like charges) Science Class VIII, Exploring Forces, p.72. It is responsible for holding atoms together, the friction between your shoes and the floor, and the flow of electricity.
3. Strong Nuclear Force: This is the "glue" of the universe. It is the strongest of all forces, but it only works over incredibly tiny distances (the size of an atomic nucleus). It overcomes the massive electrostatic repulsion between protons to keep the nucleus of an atom intact.
4. Weak Nuclear Force: Despite its name, it isn't the weakest (gravity is!), but it is responsible for certain types of radioactive decay, such as beta decay, which is crucial for the nuclear reactions that power the Sun.

For a UPSC aspirant, it is vital to distinguish these forces by their relative strength and range, as this conceptual clarity helps in both Science & Technology and Geography sections.

Force	Relative Strength	Range	Acts On
Strong Nuclear	1 (Strongest)	Very Short (Subatomic)	Nucleons (Protons/Neutrons)
Electromagnetic	10⁻²	Infinite	Charged Particles
Weak Nuclear	10⁻¹³	Very Short (Subatomic)	Elementary particles
Gravitational	10⁻³⁸ (Weakest)	Infinite	Mass

Sources: Science, Class VIII. NCERT(Revised ed 2025), Exploring Forces, p.72; Science, Class VIII. NCERT(Revised ed 2025), Exploring Forces, p.75

4. Magnetism and Magnetic Fields (intermediate)

Magnetism is a fundamental force of nature that arises from the motion of electric charges. While we often associate it with refrigerator magnets or compasses, at its core, a magnetic field is the region around a magnet or a current-carrying conductor where its influence can be felt by other magnets or moving charges Science, Class VIII, Exploring Forces, p.77. Unlike the electrostatic force, which acts between stationary charges, the magnetic force is intricately linked to motion—it determines how electric currents exert force on one another Physical Geography by PMF IAS, Earths Magnetic Field, p.65.

To visualize this invisible force, we use Magnetic Field Lines. These lines are not just arbitrary drawings; they follow very specific physical rules:

• Continuous Loops: Magnetic field lines are closed curves. Outside a magnet, they emerge from the North pole and enter the South pole. However, inside the magnet, they travel from South to North to complete the loop Science, Class X, Magnetic Effects of Electric Current, p.197.
• Density and Strength: The relative strength of a magnetic field is indicated by how crowded the lines are. Where the lines are packed tightly (like at the poles), the field is strongest.
• Non-Intersection: Two field lines never cross each other. If they did, a compass placed at the intersection would have to point in two different directions simultaneously, which is physically impossible Science, Class X, Magnetic Effects of Electric Current, p.197.

Interestingly, we can create magnetic fields that are perfectly uniform (constant in strength and direction). This is achieved using a solenoid—a long coil of insulated copper wire. Inside a current-carrying solenoid, the field lines are parallel straight lines, indicating that the magnetic field is exactly the same at all points within the cylinder Science, Class X, Magnetic Effects of Electric Current, p.201.

Feature	Bar Magnet Field	Solenoid Field (Inside)
Line Pattern	Curved loops	Parallel straight lines
Field Uniformity	Varies (Strongest at poles)	Uniform (Same everywhere inside)
Source	Intrinsic alignment of atoms	Flow of electric current

Sources: Science, Class VIII (NCERT 2025 ed.), Exploring Forces, p.77; Science, Class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.197, 201; Physical Geography by PMF IAS (1st ed.), Earths Magnetic Field, p.65

5. Newton's Law of Universal Gravitation (intermediate)

Newton’s Law of Universal Gravitation represents one of the most significant milestones in the history of science, marking the climax of the scientific revolution Themes in world history, History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119. At its core, the law states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Mathematically, this is expressed as F = G(m₁m₂)/r², where F is the gravitational force, m₁ and m₂ are the masses of the two objects, r is the distance between them, and G is the Universal Gravitational Constant. The structure of this equation is critical because it introduces the Inverse-Square Law: if you double the distance between two objects, the force doesn't just halve; it drops to one-fourth (1/2²) of its original strength. This same mathematical logic is what you will later see mirrored in Coulomb’s Law within electromagnetism.

It is vital to distinguish between mass and weight, a distinction that often trips up students. While mass is an intrinsic property of an object that remains constant everywhere, weight is specifically the gravitational pull exerted on that mass by a planet or celestial body Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.75. Because the gravitational pull of different planets varies based on their mass and radius, your weight would change significantly if you moved from Earth to Mars, even though your mass remains identical.

Feature	Mass	Weight
Nature	Intrinsic property of matter.	Force of gravitational attraction.
Constancy	Remains the same everywhere.	Changes based on the local gravity.
Equation	m	W = m × g (where g is local gravity).

In more advanced physics, we recognize that Newton's model has limits. For instance, in regions of extreme density like singularities or black holes, the classical laws of physics—including Newton's—become invalid Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.7. These intense gravitational environments are better explained by Einstein’s Theory of General Relativity, which views gravity not just as a force, but as a curvature of spacetime itself, leading to phenomena like gravitational waves caused by massive events like supernova explosions Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.5-6.

Sources: Themes in world history, History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119; Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.75; Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.5-7

6. Coulomb’s Law of Electrostatics (exam-level)

In our journey through electricity, we must understand the fundamental force that governs how charged particles interact: Coulomb’s Law. Just as gravity dictates how planets pull on one another based on their mass, Coulomb’s Law quantifies the electrostatic force of attraction or repulsion between two point charges. This law states that the magnitude of the force (F) is directly proportional to the product of the magnitudes of the charges (q₁ and q₂) and inversely proportional to the square of the distance (r) between them. This is often expressed by the formula: F = k · (q₁ · q₂) / r², where 'k' is the electrostatic constant.

The most critical aspect for competitive exams is the Inverse-Square Law relationship. Because the force is proportional to 1/r², any change in the distance between charges has a squared effect on the force. For instance, if you double the distance (r becomes 2r), the force does not just halve; it drops to (1/2)² or 1/4th of its original strength. Conversely, if you bring the charges closer by reducing the distance to half, the force increases by a factor of four. This principle is why interparticle forces are so much stronger when particles are packed tightly together, as seen in the structure of solids Science, Class VIII NCERT, Particulate Nature of Matter, p.113.

It is also important to note the units involved. Charge is measured in Coulombs (C). To give you a sense of scale, the potential difference of 1 Volt is defined as 1 Joule of work done per 1 Coulomb of charge Science, Class X NCERT, Electricity, p.173. Whether the force is attractive (between opposite charges) or repulsive (between like charges), the mathematical rule remains the same. In a vacuum or air, this force is incredibly potent at short distances, acting as the "glue" that holds atoms and molecules together.

Sources: Science, Class VIII NCERT, Particulate Nature of Matter, p.113; Science, Class X NCERT, Electricity, p.173

7. Calculating Force Changes using Proportionality (exam-level)

In the study of physics, particularly when dealing with non-contact forces like electricity and magnetism, we often encounter forces that act over a distance without physical touch Science, Class VIII, Exploring Forces, p.69. To master these concepts for the exam, you don't always need to calculate exact values; instead, you must understand proportionality. The most critical rule here is the Inverse-Square Law. This law states that the force (F) between two point charges is inversely proportional to the square of the distance (r) between them (F ∝ 1/r²). This means that as the distance increases, the force weakens—but it weakens much faster than the distance grows.

Let’s look at how to apply this logic systematically. If you increase the distance between two objects by a factor of 'n', the force is reduced by a factor of n². For example, if you double the distance (n = 2), the force becomes 1/(2²) or 1/4th of the original. If you triple the distance (n = 3), the force drops to 1/(3²) or 1/9th. This principle of proportionality is a recurring theme in science; for instance, the heat produced in a resistor is also governed by squared proportionality—specifically, it is directly proportional to the square of the current Science, Class X, Electricity, p.189.

To solve these problems quickly in a competitive setting, always identify the ratio of change first. If an object is moved from an initial distance of 5 cm to a final distance of 10 cm, the distance has effectively doubled (10/5 = 2). Squaring this change factor (2² = 4) and taking its reciprocal (1/4) immediately gives you the new force relative to the old one. This mental shortcut allows you to bypass complex constants and units, focusing purely on the relationship between the variables.

Sources: Science, Class VIII (NCERT), Exploring Forces, p.69; Science, Class X (NCERT), Electricity, p.189

8. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamentals of Coulomb’s Law, this question serves as the perfect litmus test for your understanding of the inverse-square relationship. In your previous modules, you learned that the electrostatic force between two point charges is not just dependent on the magnitude of the charges, but is critically sensitive to the distance separating them. This specific PYQ requires you to synthesize the concept of proportionality with a careful reading of the physical change described: an increase in separation distance from 5 cm to a new total of 10 cm.

To arrive at the correct answer, reduced to one-fourth, you must focus on the ratio of change rather than the absolute values. Since the second body is shifted "another 5 cm," the total distance doubles (from 5 cm to 10 cm). Because the force is inversely proportional to the square of the distance ($F \propto 1/r^2$), doubling the distance ($2r$) results in the force being multiplied by $1/2^2$, which is $1/4$. This step-by-step reasoning—identifying the multiplier of change first and then applying the inverse-square rule—is a hallmark of the analytical thinking required for UPSC General Science.

UPSC frequently includes "trap" options to catch students who apply the law incompletely. Option (B) halved is the most common pitfall; it targets students who recognize the inverse relationship but forget to square the distance. Options (A) and (C) can be immediately discarded through qualitative reasoning: since the bodies are being moved further apart, the force of repulsion must decrease, making any option that suggests an increase logically impossible. Mastering these distinctions ensures you won't be misled by the phrasing of the question, as emphasized in NCERT Class 12 Physics.