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JEE ADVANCED HOOKS LAW AND COULMBS LAW PRACTISE QUESTION

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Two identical metallic blocks are connected by a light metallic spring with:
Spring constant = k
Unstretched length = Li

A battery gradually supplies charge to the system, such that the total charge transferred is Q . The charge is slowly distributed over time, ensuring that at any moment, each block has equal charge q/2.

Due to electrostatic repulsion, the blocks move apart, stretching the spring to a new **equilibrium length L .

QuestioN
1. Determine the total work done by the battery in charging the system and stretching the spring.
2. Explain how the work done by the battery is stored in the system.
3. Derive the energy balance equation considering electrostatic and elastic potential energy.
Given
Charge is added gradually by the battery.
Blocks remain in equilibrium at all times.
Battery is the only external energy source.
Neglect any external forces apart from the electrostatic force and the spring force.


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he electrostatic force pushes the blocks apart, increasing their separation.
The spring resists the motion, storing elastic potential energy.
The battery provides energy, which is distributed between the electrostatic potential energy of the charges and the elastic potential energy of the stretched spring.
The system remains in equilibrium throughout the process since charge is added gradually.

Summary of Key Concepts Used in the Solution

✔ Electrostatic Force: Repulsion between charged blocks increases separation.
✔ Elastic Potential Energy: The stretched spring stores mechanical energy.
✔ Work Done by Battery: Converts chemical energy into electrostatic and elastic energy.
✔ Energy Conservation: The total supplied energy is divided between electrostatic and mechanical energy.



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🚀 *Learn how electrostatic force and spring mechanics interact in this physics problem!* In this video, we solve a conceptual **Young’s Modulus and Hooke’s Law numerical**, where two metallic blocks are connected by a spring and charged by a battery.

💡 *Topics Covered:*
✅ Work Done by Battery in an Electrostatic System
✅ Energy Stored in a Stretched Spring
✅ Electrostatic Repulsion & Hooke’s Law
✅ Complete Solution for IIT JEE & NEET Physics

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