Class 12 · Physics

NCERT Solutions: Electric Charges and Fields (Class 12 Physics)

Coulomb's law, electric field, Gauss's law, and worked practice problems for the Electrostatics chapter in Class 12 Physics.

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Chapter overview

This chapter introduces electric charge, Coulomb’s law, the electric field concept, and Gauss’s law - the foundation for all of electrostatics and, later, current electricity.

Key formulas

  • Coulomb’s law: F = k q₁q₂ / r², where k = 1/(4πε₀) ≈ 9 × 10⁹ N·m²/C²
  • Electric field due to a point charge: E = kq / r²
  • Electric field due to a dipole (axial line): E = 2kp / r³ (for r >> a)
  • Gauss’s law: Φ = q_enclosed / ε₀

Worked practice problem 1 — Coulomb’s law

Question: Two point charges of +2 μC and +3 μC are placed 30 cm apart in air. Find the force between them.

Solution:

F = k q₁q₂ / r² = (9 × 10⁹)(2 × 10⁻⁶)(3 × 10⁻⁶) / (0.3)²
F = (9 × 10⁹)(6 × 10⁻¹²) / 0.09
F = 0.54 / 0.09 = 6 × 10⁻¹ N = 0.6 N

Answer: The force is 0.6 N, repulsive (since both charges are positive).

Worked practice problem 2 — Electric field

Question: Find the electric field at a point 20 cm from a point charge of 5 μC.

Solution:

E = kq / r² = (9 × 10⁹)(5 × 10⁻⁶) / (0.2)²
E = 45000 / 0.04 = 1.125 × 10⁶ N/C

Answer: The electric field at that point is 1.125 × 10⁶ N/C, directed radially away from the charge (since it is positive).

Worked practice problem 3 — Gauss’s law

Question: A charge of 8.85 × 10⁻⁸ C is enclosed by a spherical Gaussian surface. Find the total electric flux through the surface. (Take ε₀ = 8.85 × 10⁻¹² C²/N·m²)

Solution:

Φ = q / ε₀ = (8.85 × 10⁻⁸) / (8.85 × 10⁻¹²) = 10⁴ N·m²/C

Answer: The total flux through the surface is 10,000 N·m²/C, independent of the shape or size of the surface (as long as it encloses the same charge).

Common mistakes to avoid

  • Forgetting to convert μC to C before substituting into formulas (a factor-of-10⁶ error is easy to make).
  • Mixing up the direction of the electric field for positive vs. negative source charges.
  • Assuming Gauss’s law only applies to spherical surfaces - it holds for any closed surface.

Looking for the official textbook PDF for this chapter? Visit our Class 12 NCERT Books page for the direct download link.