Solveeit Logo
Login

Question

Question: Statement-l: The energy stored in electrostatic field of a system of charges depends only on the con...

Statement-l: The energy stored in electrostatic field of a system of charges depends only on the configuration of charges and not on the method used to assemble the system.

Statement-II: The electrostatic potential energy of a system of charges is a state function, means its value depends only on the configuration of the charges and not on path taken to assemble the system.

A

Both Statement I and Statement II are true, and Statement II is the correct explanation of Statement I.

B

Both Statement I and Statement II are true, but Statement II is not the correct explanation of Statement I.

C

Statement I is true but Statement II is false.

D

Statement I is false but Statement II is true.

Answer

Both Statement I and Statement II are true, and Statement II is the correct explanation of Statement I.

Explanation

Solution

The core concept here is the nature of electrostatic force and its relation to potential energy.

  1. Electrostatic Force is Conservative: Electrostatic force is a conservative force. This means that the work done by or against this force in moving a charge from one point to another depends only on the initial and final positions, and not on the path taken.

  2. Electrostatic Potential Energy Definition: The electrostatic potential energy of a system of charges is defined as the work done by an external agency in assembling the charges from infinity (where their interaction energy is zero) to their current configuration, without any change in kinetic energy (i.e., without acceleration).

  3. Statement-I Analysis: "The energy stored in electrostatic field of a system of charges depends only on the configuration of charges and not on the method used to assemble the system." Since the electrostatic force is conservative, the work done to assemble the charges (which is stored as potential energy) is independent of the path taken or the method used to bring the charges to their final positions. It only depends on the final arrangement (configuration) of the charges. Thus, Statement-I is true.

  4. Statement-II Analysis: "The electrostatic potential energy of a system of charges is a state function, means its value depends only on the configuration of the charges and not on path taken to assemble the system." A "state function" (or point function) is a property of a system that depends only on the current state of the system, not on the path taken to reach that state. Because electrostatic forces are conservative, the electrostatic potential energy precisely fits this definition. Its value is uniquely determined by the spatial arrangement (configuration) of the charges, regardless of how they were brought to that arrangement. Thus, Statement-II is true.

  5. Relationship between Statements: Statement-II explains why Statement-I is true. The fact that electrostatic potential energy is a state function (due to the conservative nature of the electrostatic force) directly implies that it depends only on the configuration and not on the method of assembly. Therefore, Statement-II is the correct explanation for Statement-I.

Conclusion: Both Statement-I and Statement-II are true, and Statement-II is the correct explanation of Statement-I.