If two conducting spheres are separately charged and then brought in contact—

1. The Nature of Electric Charge (basic)

At its most fundamental level, electric charge is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Everything around us is made of atoms, which contain subatomic particles: protons (carrying a positive charge) and electrons (carrying a negative charge). In a neutral state, these charges are balanced. However, when an object gains or loses electrons, it becomes a charged object. As observed in nature, a charged object can exert a force even without physical contact, such as when a charged comb attracts tiny pieces of paper Science, Class VIII, Exploring Forces, p.70.

There are two primary rules governing the behavior of these charges:

• Interaction: Like charges (positive-positive or negative-negative) repel each other, while opposite charges attract. This is seen clearly in chemical bonding, where a sodium atom loses an electron to become a positive ion (Na⁺) and a chlorine atom gains that electron to become a negative ion (Cl⁻). The resulting electrostatic force of attraction holds them together Science, Class X, Metals and Non-metals, p.47.
• Conservation of Charge: This is a cornerstone of physics. Charge can neither be created nor destroyed; it can only be transferred from one body to another. The total charge of an isolated system always remains constant.

When two conductors with different amounts of charge are brought into contact, charges will flow between them. This movement is driven by a potential difference—think of it like water flowing from a high tank to a low tank. Charges move from a body at a higher potential to one at a lower potential until their potentials equalize Science, Class X, Electricity, p.173. While the total charge is conserved during this redistribution, the total energy is often not, as some energy is dissipated as heat due to the resistance of the materials Science, Class X, Electricity, p.188.

Sources: Science, Class VIII (NCERT Revised ed 2025), Exploring Forces, p.70; Science, Class X (NCERT 2025 ed.), Metals and Non-metals, p.47; Science, Class X (NCERT 2025 ed.), Electricity, p.173; Science, Class X (NCERT 2025 ed.), Electricity, p.188

2. Conductors, Insulators, and Electron Flow (basic)

To understand electricity, we must first look at the atomic level. All matter is made of atoms, which contain electrons. In some materials, these electrons are tightly bound to their parent atoms and cannot move easily; we call these insulators. In other materials, particularly metals, the outermost electrons are loosely held and can wander freely between atoms; these are our conductors. Metals like silver, copper, and gold are the most efficient conductors because they possess a high density of these 'free electrons' Science-Class VII, Electricity: Circuits and their Components, p.36. Conversely, materials like rubber, plastic, and ceramics offer immense resistance to the movement of electrons, making them ideal for insulating wires to protect us from electric shocks Science, Class X, Electricity, p.177.

When two conductors are brought into contact, a fascinating process occurs: charge redistribution. If one conductor has more electrical 'pressure' (higher potential) than the other, electrons will flow from one to the other until their potentials equalize. A critical principle here is the Conservation of Charge: while charges move from one body to another, the total amount of charge across both bodies remains exactly the same—it is neither created nor destroyed. However, do not confuse this with energy conservation. As electrons flow through the resistance of the conductors, some electrical energy is inevitably converted into heat, meaning the total electrostatic energy after contact is usually less than it was before Science, Class X, Electricity, p.188.

In our daily lives, we see this science in action within our home wiring. We use copper for the actual wire because it is a great conductor and relatively affordable, but we wrap it in plastic (an insulator) for safety. In a standard AC supply, you will notice color-coded insulation: Live wires (red), Neutral wires (black), and Earth wires (green) Science, Class X, Magnetic Effects of Electric Current, p.206. The Earth wire is a safety conductor designed to carry stray charges safely into the ground, preventing the metallic body of an appliance from becoming 'live' and dangerous.

Feature	Conductors	Insulators
Electron Mobility	High (Free electrons)	Low (Bound electrons)
Resistance	Low	Very High
Examples	Copper, Silver, Aluminum, Human Body	Rubber, Glass, Plastic, Dry Wood

Sources: Science-Class VII, Electricity: Circuits and their Components, p.36; Science, class X, Electricity, p.177; Science, class X, Electricity, p.188; Science, class X, Magnetic Effects of Electric Current, p.206

3. Electric Potential and Potential Difference (intermediate)

To understand electricity, we must first understand what makes charges move. Imagine a flat pipe filled with water; the water stays still. But if you tilt the pipe or use a pump to create a pressure difference, the water flows. In the world of physics, Electric Potential is the "electrical pressure" that pushes charges through a conductor. It is essentially the amount of electric potential energy a unit charge would have at a specific point in space.

In a practical circuit, we focus on the Electric Potential Difference (often simply called Voltage). We define this as the work done (W) to move a unit charge (Q) from one point to another. This relationship is expressed by the fundamental formula:

V = W / Q

The SI unit for potential difference is the Volt (V), named after Alessandro Volta. One volt is defined as the potential difference between two points when 1 Joule of work is done to move a charge of 1 Coulomb from one point to the other Science, class X (NCERT 2025 ed.), Chapter 11, p.173. This "push" is maintained in our gadgets by devices like batteries or cells, which use chemical energy to keep one terminal at a higher potential than the other Science, class X (NCERT 2025 ed.), Chapter 11, p.174.

Concept	Definition	Unit
Electric Potential	The energy per unit charge at a specific point.	Volt (V)
Potential Difference	The work done to move a unit charge between two points.	Volt (V)

An advanced but crucial nuance to remember is what happens when two charged bodies are connected. Charges will naturally flow from the body at higher potential to the one at lower potential until their potentials equalize. While the total charge is conserved during this process (it is neither created nor destroyed), the total electrostatic energy is generally not conserved. Some energy is inevitably lost as heat due to the resistance of the wire or as sparks during the transfer Science, class X (NCERT 2025 ed.), Chapter 11, p.188.

Sources: Science, class X (NCERT 2025 ed.), Chapter 11: Electricity, p.173; Science, class X (NCERT 2025 ed.), Chapter 11: Electricity, p.174; Science, class X (NCERT 2025 ed.), Chapter 11: Electricity, p.188

4. Capacitance: Ability to Store Charge (intermediate)

At its heart, capacitance is the measure of an object's ability to store electric charge. Imagine it as the 'electrical volume' of a container; just as a larger tank can hold more water at a certain pressure, a conductor with higher capacitance can hold more charge for a given electrical potential. In our study of circuits, we find that moving a charge (Q) between two points requires work (W), which is defined by the potential difference (V) Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p. 173. Capacitance (C) is the constant that links these, expressed as C = Q/V.

When two charged conducting spheres are brought into contact, a redistribution of charge occurs. Nature moves toward equilibrium: charges flow from the sphere with higher potential to the one with lower potential until their potentials equalize. A vital principle to remember here is the Law of Conservation of Charge. The total charge of the system remains constant throughout this process; it is merely shared between the two bodies based on their respective sizes or capacities.

However, there is a catch that often trips up students: while charge is conserved, total electrostatic energy is generally not. As charges redistribute, the 'flow' encounters resistance, which converts some electrical energy into heat Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p. 188. You might even observe this energy loss as a small spark. Consequently, the final energy of the combined system is almost always lower than the sum of their initial energies, even though every single electron is accounted for.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.173; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.188

5. Joule’s Law and Heating Effects (intermediate)

When we look at electricity, we often focus on the movement of charge to do work, like spinning a motor. However, at the microscopic level, as electrons drift through a conductor, they constantly collide with the atoms and ions of the material. These collisions transfer kinetic energy from the electrons to the lattice structure of the conductor, causing its temperature to rise. This transformation of electrical energy into thermal energy is what we call the heating effect of electric current. In a purely resistive circuit, the entire energy supplied by the source is dissipated as heat Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.188.

This phenomenon is quantified by Joule’s Law of Heating. If a current (I) flows through a resistor (R) for a time (t), the heat produced (H) is given by the formula: H = I²Rt. This law tells us three crucial things about heat generation:

• It is directly proportional to the square of the current (I²). This means doubling the current results in four times the heat.
• It is directly proportional to the resistance (R) for a given current.
• It is directly proportional to the time (t) for which the current flows Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.189.

While this heating is an inevitable "loss" in devices like fans or power cables, it is the fundamental principle behind many of our most common appliances. For instance, in an electric bulb, the filament (usually made of tungsten due to its high melting point) is designed to retain heat until it becomes so hot that it emits light. Similarly, electric irons, toasters, and heaters intentionally use high-resistance alloys to maximize this heating effect Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.190. Understanding this relationship is vital for engineers designing safe circuits and for us to understand why our gadgets get warm during use.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.188; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.189; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.190

6. The Law of Conservation of Charge (exam-level)

The Law of Conservation of Charge is a fundamental pillar of physics, stating that the total electric charge in an isolated system remains constant over time. Charge can neither be created nor destroyed; it can only be transferred from one body to another. In any interaction—whether it is rubbing two objects together or connecting two conductors—the algebraic sum of the positive and negative charges remains unchanged. As we see in Science, Class X (NCERT 2025 ed.), Electricity, p. 173, just as water requires a pressure difference to flow through a tube, electric charges require a potential difference to move between two points.

Consider a classic exam scenario: two conducting spheres with different initial charges are brought into contact. Charge will flow between them because of the difference in their "electric pressure" or potential. This redistribution continues until their potentials equalize. While the charges redistribute based on the capacity (size) of each sphere, the total charge (Q₁ + Q₂) before contact will exactly equal the total charge after contact. However, a common misconception is that energy is also conserved in this process. In reality, while charge is strictly conserved, the total electrostatic energy typically decreases. This is because the movement of charge against the resistance of the material generates heat (H = VIt), as noted in Science, Class X (NCERT 2025 ed.), Electricity, p. 188, and may even result in electromagnetic radiation or sparks.

The final distribution of charge depends on the capacitance of the spheres. If the spheres are identical in size, they will share the total charge equally. If they are of different sizes, the larger sphere will hold more charge at equilibrium, even though both will eventually reach the same electric potential.

Property	Status during Redistribution	Reason
Total Charge	Conserved	Fundamental law of nature; charge is only transferred.
Total Energy	Not Conserved	Lost as heat (resistance) or light (sparks).
Electric Potential	Equalized	Flow stops only when potential difference is zero.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.173; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.188

7. Redistribution of Charge and Energy Loss (exam-level)

When we bring two conductors with different electric potentials into contact, a fascinating physical process begins: the redistribution of charge. Think of it like connecting two water tanks with different water levels; water will naturally flow from the higher level to the lower level until the levels—or in our case, the potentials—are equal. In electrostatics, charge flows from the body at a higher potential to the one at a lower potential until they reach a common potential.

During this process, the Principle of Conservation of Charge remains absolute. The total charge before contact ($Q₁ + Q₂$) must equal the total charge after redistribution. As highlighted in Science, Class X (NCERT 2025 ed.), Chapter 11, p. 173, charge is a fundamental property that doesn't just disappear. However, the final distribution of this charge depends on the capacitance (size and shape) of the conductors. If one sphere is much larger than the other, it will "hold" more of the total charge once the potentials equalize.

Interestingly, while charge is conserved, electrostatic energy is NOT conserved. Whenever charge flows through a medium (like a connecting wire), it encounters resistance, leading to the heating effect of electric current. According to the relationship $H = VIt$, energy is dissipated as heat during the transition Science, Class X (NCERT 2025 ed.), Chapter 11, p. 188. Even in an ideal scenario with no resistance, energy is lost in the form of electromagnetic radiation or sparks at the moment of contact. Therefore, the total energy of the system after redistribution is always less than the total energy before contact.

Quantity	Status during Redistribution	Reason
Total Charge	Conserved	Charge cannot be created or destroyed.
Total Energy	Decreased	Lost as heat ($H = VIt$) or radiation.
Potential	Equalized	Flow stops when potential difference is zero.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.173; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.188

8. Solving the Original PYQ (exam-level)

This question is a classic application of the Law of Conservation of Charge and the dynamics of electric potential. Having just mastered the building blocks of electrostatics, you should recognize that when two conductors are joined, they form a single system. The fundamental principle here is that charge cannot be created or destroyed; it merely redistributes itself until electrostatic equilibrium is reached. This equilibrium occurs when the potential difference between the two spheres becomes zero, meaning they reach a common potential. As a result, the total charge on the two spheres is conserved, which makes option (B) the only logically sound choice across all physical scenarios.

To arrive at this answer, think like a physicist: what happens during that split second of contact? As charges move from the sphere of higher potential to the one of lower potential, they encounter resistance. According to the concepts of the Heating Effect of Electric Current found in Science, Class X (NCERT 2025 ed.), this movement of electrons inevitably converts some electrostatic potential energy into thermal energy (heat) or even electromagnetic radiation if a spark occurs. Therefore, while charge is conserved, total energy is not conserved within the electrostatic field because some of it is dissipated into the environment. This realization allows you to confidently eliminate options (A) and (C).

Finally, do not fall for the mathematical trap in option (D). The final potential is a weighted average based on the capacitance (which depends on the radii) of the spheres, not a simple arithmetic mean. The potentials only average out perfectly if the spheres are identical in size. UPSC often uses such "special case" distractors to test if you understand the general rule versus a specific condition. By sticking to the universal law of conservation, you avoid these common pitfalls and secure the marks.