Chapter: Electrostatics | CUET Level | PHYSICS

Electrostatics

1. Electric Charge

• Electric charge is a fundamental property of matter that produces electric and magnetic effects.
• There are two types: Positive (+) and Negative (−).
• Like charges repel each other; unlike charges attract each other.
• Quantization of Charge: q = ±ne, where n is an integer and e = 1.6 × 10⁻¹⁹ C (elementary charge).
• Conservation of Charge: The total charge in an isolated system remains constant. Charge can neither be created nor destroyed.

2. Coulomb’s Law

The electrostatic force between two stationary point charges is given by:

$$F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2} = k \frac{q_1 q_2}{r^2}$$

• k = 9 × 10⁹ N m² C⁻² (in vacuum).
• The force is attractive if charges are opposite and repulsive if they are similar.
• In a medium: F = F₀ / εᵣ, where εᵣ is the relative permittivity (dielectric constant).

3. Electric Field

• Electric field intensity (E) at a point is the force experienced by a unit positive test charge placed at that point: E = F / q₀
• Electric field due to a point charge q at distance r:

$$E = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2} \hat{r}$$

• Principle of Superposition: The total electric field is the vector sum of the fields due to individual charges.
• Electric Field Lines: Emerge from positive charges and terminate on negative charges. Parallel lines indicate uniform field.

4. Electric Flux and Gauss’s Law

• Electric flux: Φ = E ⋅ A (for plane surface) or Φ = ∫ E ⋅ dA.
• Gauss’s Law: The total electric flux through any closed surface is equal to (1/ε₀) times the total charge enclosed by the surface.

$$\oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\text{enclosed}}}{\epsilon_0}$$

• Very useful for calculating electric field in cases of symmetric charge distributions (spherical, cylindrical, or plane symmetry).

5. Electric Potential

• Electric potential (V) at a point is the work done in bringing a unit positive charge from infinity to that point.
• Electric potential due to a point charge q at distance r:

$$V = \frac{1}{4\pi\epsilon_0} \frac{q}{r}$$

• Potential is a scalar quantity. SI unit is Volt (V).
• Electrostatic Potential Energy: U = qV For two charges: U = (1/(4πε₀)) (q₁q₂ / r)
• Relation between field and potential: E = – dV/dr (Electric field is the negative gradient of potential).

6. Electric Dipole

• An electric dipole consists of two equal and opposite charges separated by a small distance (2a).
• Dipole moment p = q × 2a (direction from negative to positive charge).
• Electric field due to dipole:
  • On axial line: E = (1/(4πε₀)) (2p / r³)
  • On equatorial line: E = (1/(4πε₀)) (p / r³)
• Torque on a dipole in uniform electric field: τ = p × E

7. Properties of Conductors in Electrostatics

• Inside a conductor (in electrostatic equilibrium), E = 0.
• Electric field just outside the surface is perpendicular to the surface.
• Excess charge resides only on the outer surface of the conductor.
• The entire conductor is at the same potential (equipotential surface).

8. Important Formula Summary

• Coulomb’s Law: $F = k \frac{q_1 q_2}{r^2}$
• Electric Field (point charge): $E = k \frac{q}{r^2}$
• Electric Potential (point charge): $V = k \frac{q}{r}$
• Gauss’s Law: $\Phi = \frac{Q}{\epsilon_0}$
• Capacitance of parallel plate capacitor: $C = \frac{\epsilon_0 A}{d}$ (With dielectric: C' = κC)