JEE Physics Notes: Electrostatic Potential and Capacitance

Introduction

Electrostatic potential and capacitance are fundamental concepts in electrostatics, dealing with electric potential energy, potential difference, and the ability of conductors to store charge.

1. Electrostatic Potential

• Definition: The electrostatic potential at a point is the work done in bringing a unit positive charge from infinity to that point in an electric field.
• Formula: V = W/q, where V is potential, W is work done, and q is charge.
• SI Unit: Volt (V).
• Potential Due to a Point Charge: V = kQ/r, where Q is the charge and r is the distance from the charge.

2. Potential Difference

• Definition: The work done in moving a unit positive charge from one point to another in an electric field.
• Formula: V = Ed, where E is the electric field and d is the displacement.

3. Electrostatic Potential Energy

• Definition: The work done in assembling a system of charges.
• Formula for Two Charges: U = kQ₁Q₂/r, where Q₁ and Q₂ are two charges and r is the separation.

4. Equipotential Surfaces

• Definition: Surfaces where the electric potential is the same everywhere.
• Properties:
  • No work is done when a charge moves along an equipotential surface.
  • Equipotential surfaces are perpendicular to electric field lines.

5. Capacitance

• Definition: The ability of a system to store electric charge.
• Formula: C = Q/V, where C is capacitance, Q is charge, and V is potential difference.
• SI Unit: Farad (F).

6. Capacitors

• Definition: Devices that store electric charge and energy.
• Parallel Plate Capacitor: C = ε₀A/d, where ε₀ is permittivity, A is plate area, and d is separation.
• Effect of Dielectric: Increases capacitance by a factor of dielectric constant K.

7. Combination of Capacitors

• Series Combination: 1/Cₑ = 1/C₁ + 1/C₂ + ...
• Parallel Combination: Cₑ = C₁ + C₂ + ...

8. Energy Stored in a Capacitor

• Formula: U = (1/2) CV².
• Energy is stored in the electric field between capacitor plates.

Conclusion

Electrostatic potential and capacitance are crucial in understanding electric fields, charge storage, and energy in electric circuits. These concepts are essential for JEE Physics preparation.