Introduction:

The potential energy in an external field is a cornerstone topic in Class 12 Physics, forming the foundation for understanding mechanics, gravitation, and electrostatics. This concept explores the work done by or against a field, storing energy in a system. From gravitational to electric fields, potential energy is crucial in analyzing physical systems' behavior.

Detailed Study Notes on Potential Energy in an External Field:

What is Potential Energy?

Potential energy is the energy possessed by a body due to its position or configuration in a force field. It is the energy stored in a system that can be converted into other forms, such as kinetic energy.

Expression for Potential Energy in an External Field:

1. General Formula:

The potential energy (U) in an external field is expressed as:

U = - ∫ F · dr

where:

- F: Force acting on the body

- dr: Displacement vector

2. Gravitational Potential Energy:

In a uniform gravitational field:

U = mgh

where:

- m: Mass of the body

- g: Acceleration due to gravity

- h: Height from the reference point

3. Electric Potential Energy:

For a charge q in an electric field E:

U = qEd

where d is the displacement in the field direction.

Work-Energy Theorem and Potential Energy:

The work done by an external force changes a system's potential energy.

W = ΔU

Potential Energy Curve and Stability:

- Stable Equilibrium: Point where potential energy is minimum.

- Unstable Equilibrium: Point where potential energy is maximum.

- Neutral Equilibrium: Constant potential energy across positions.

Read Also: Potential Energy of a System of Charges: Class 12 Physics Notes

Applications of Potential Energy in External Fields:

1. Gravitational Systems: Satellites, planetary motion, pendulums.

2. Electric Fields: Capacitors, charged particles in electric fields.

3. Elastic Systems: Springs and Hooke’s Law.

Key Differences Between Gravitational and Electric Potential Energy:

Conclusion:

Understanding potential energy in external fields is essential for solving physics problems in mechanics, electrostatics, and gravitation. The concept not only explains the storage and transfer of energy in systems but also offers insights into stability and equilibrium in various physical scenarios.