Problem 125 - Master Resource Book in JEE Main Physics

Question

Assertion-Reason type. Each of these contains two Statements : Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion When charges are shared between two bodies, there occurs no loss of charge. However, there is a loss in electrical energy. Reason Electrostatic potential energy does not come under the preview of the conservation law of energy.

Step-by-Step Solution

Answer

(c) Assertion is true but Reason is false.

Step 1: Evaluate the Assertion

The assertion states that when charges are shared between two bodies, there is no loss of charge but there is a loss in electrical energy. This assertion is true because charge is conserved; it is only redistributed between the bodies. However, the energy before and after charge transfer is different because energy is stored in the form of electrostatic potential energy, and some energy might be lost as heat during redistribution.

Step 2: Evaluate the Reason

The reason claims that electrostatic potential energy does not fall under the conservation law of energy. This statement is false because electrostatic potential energy, like all forms of energy, is subject to the conservation law of energy. It can, however, be transformed into another form like kinetic energy or thermal energy during interactions.

Step 3: Determine the Correct Choice

Since the Assertion is true, but the Reason provided is false and cannot explain the assertion correctly, the correct choice is (c). The assertion is correct independently of the reason's incorrect explanation.

Key Concepts

Conservation of Charge

The conservation of charge is a fundamental principle in physics stating that the total electric charge in a closed system remains constant over time. In simpler terms, this means that charge can neither be created nor destroyed. When two objects interact electrically, charges are merely transferred from one object to another.

• For example, when you rub a balloon on your hair, electrons transfer from your hair to the balloon, charging the balloon negatively while your hair becomes positively charged. Despite this transfer, the total charge in the system remains unchanged.
• Similarly, when charges are shared between two bodies, as mentioned in the assertion, there's no loss in the total amount of charge. The charge is simply redistributed between the bodies.

This conceptualizes the static condition of charge, ensuring that the universe always maintains its electrical balance. Understanding this concept helps explain why electrical circuits require a closed loop to transfer energy efficiently.

Electrostatic Potential Energy

Electrostatic potential energy is the energy stored due to the position and interaction of charges within a system. When two charges are placed in each other's vicinity, they exert a force on one another, and work must be done to bring them closer or farther apart. This work is stored as electrostatic potential energy.

• This energy depends on the magnitude of the charges and the distance between them. The closer the charges, the higher the electrostatic potential energy if they have opposite signs. With like charges, the energy increases as they are pushed together due to the repulsive force.
• Unlike kinetic energy which is energy of motion, electrostatic potential energy is a positional form of potential energy, emphasizing the unique nature of interactions between charged particles.

An important aspect of electrostatic potential energy is its ability to convert into other forms of energy, such as kinetic energy, when the charges move under the influence of electric forces. This conversion is an integral part of energy conservation in physics.

Conservation of Energy Law

The conservation of energy law is one of the core tenets of physics which states that the total energy of an isolated system remains constant over time. Energy cannot be created or destroyed; it can only change forms.

• For instance, in a pendulum swinging, the energy transforms between potential energy at the highest points and kinetic energy at the lowest point, yet the total energy remains the same.
• This principle applies universally, encompassing all forms of energy including electrostatic potential energy, mechanical energy, thermal energy, and more.
• In the context of charges sharing and redistributing, while the total charge remains constant due to charge conservation, the total energy may change as potential energy converts to other energies such as heat due to resistance in the material.

Understanding energy conservation allows us to predict how systems behave, ensuring that all energy transitions and transformations are accounted for in any physical process.