Electrostatic Potential & Capacitance

Electrostatic Potential and Capacitance for JEE/NEET

Concept: Electrostatic potential (V) at a point in an electric field is the work done per unit positive charge in bringing a small test charge from infinity to that point against the electrostatic force without any acceleration.
Scalar Quantity: It’s a scalar quantity, meaning it only has magnitude and no direction.
Unit: The SI unit of electric potential is the volt (V), where 1 V = 1 J/C (joule per coulomb).
Potential Difference: The potential difference between two points is the work done per unit charge in moving a charge between those points.
Relationship with Electric Field: The electric field (E) is the negative gradient of the electric potential (V). This means the electric field points in the direction of decreasing potential.
- E = -∇V
Potential due to a Point Charge: The electric potential (V) at a distance ‘r’ from a point charge ‘q’ is given by: V=kq/r
Potential due to a System of Charges: The electric potential at a point due to a system of charges is the algebraic sum of the potentials due to each individual charge.

Equipotential Surfaces

Definition: An equipotential surface is a surface on which the potential is constant at every point.
Properties:
- No work is done in moving a charge from one point to another on an equipotential surface.
- Electric field lines are always perpendicular to equipotential surfaces.
- For a point charge, the equipotential surfaces are concentric spheres.
- For a uniform electric field, the equipotential surfaces are planes perpendicular to the field lines.

Electrostatic Potential Energy

Concept: Electrostatic potential energy (U) is the energy possessed by a system of charges due to their positions relative to each other.
Work Done: The work done in assembling a system of charges is equal to the electrostatic potential energy of the system.
Potential Energy of Two Point Charges: The electrostatic potential energy (U) of two point charges q1 and q2 separated by a distance ‘r’ is:
- U = k (q1 * q2) / r

Capacitance

Concept: Capacitance (C) is the ability of a conductor to store electric charge.
Definition: It is the ratio of the magnitude of the charge (Q) on the conductor to the potential difference (V) across it.
- C = Q/V
Unit: The SI unit of capacitance is the farad (F), where 1 F = 1 C/V (coulomb per volt).
Capacitor: A capacitor is a device specifically designed to store electric charge. It typically consists of two conductors separated by an insulator (dielectric).

Types of Capacitors

Parallel Plate Capacitor: Two parallel conducting plates separated by a distance. The capacitance of a parallel plate capacitor is given by:
- C = ε₀A/d where:
  - ε₀ is the permittivity of free space
  - A is the area of each plate
  - d is the distance between the plates
Other Types: Spherical capacitors, cylindrical capacitors, etc.

Dielectrics

Effect: Introducing a dielectric material between the plates of a capacitor increases its capacitance.
Dielectric Constant: The dielectric constant (K) of a material is a measure of how much it increases the capacitance.
- C = Kε₀A/d

Combination of Capacitors

Series Combination: When capacitors are connected in series, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances.
Parallel Combination: When capacitors are connected in parallel, the equivalent capacitance is the sum of the individual capacitances.

Energy Stored in a Capacitor

Energy: A charged capacitor stores electrical potential energy.
Formula: The energy (U) stored in a capacitor is given by:
- U = 1/2 CV² = 1/2 QV = 1/2 Q²/C

Electrostatic Potential and Capacitance for JEE/NEET- Applications of Capacitors

Capacitors have numerous applications in electronics and electrical engineering, including: