NCERT Solutions for Class 12 Physics Chapter 1 Electric Charges and Fields
NCERT Solutions for Class 12 Physics Chapter 1 Electric Charges and Fields provides detailed revision notes, key formulas, derivations, and step-by-step textbook solutions covering electric charges, Coulomb's Law, electric field, dipoles, electric flux, and Gauss's Law.
Overview of Topics & Subtopics (Click to Jump)
1. Electric Charge & Basic Properties
Short Note:
• Electric Charge (q): Fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. SI unit is Coulomb (C).
• Quantization of Charge: The total charge on a body is always an integral multiple of the basic unit of charge e: q = ±ne (where e = 1.6 × 10⁻¹⁹ C, n = 1, 2, 3...).
• Conservation of Charge: The net electric charge of an isolated system remains constant during any physical or chemical process.
• Additivity of Charge: Total charge of a system is the algebraic sum of all individual point charges present anywhere on the body.
2. Coulomb's Law & Principle of Superposition
Short Note:
• Coulomb's Law: The electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
- Formula: F = (1 / 4πε₀) × (|q₁ q₂| / r²), where 1 / 4πε₀ ≈ 9 × 10⁹ N·m²/C².
• Permittivity: ε₀ is the permittivity of free space (8.854 × 10⁻¹² C²/N·m²). In a medium with dielectric constant K, F_medium = F_vacuum / K.
• Principle of Superposition: Force on any charge due to a number of other charges is the vector sum of all the forces exerted on it by the other charges taken one at a time.
3. Electric Field & Electric Field Lines
Short Note:
• Electric Field (E): Force experienced per unit positive test charge placed at a point: E = F / q₀. SI unit is N/C or V/m.
• Electric Field due to Point Charge: E = (1 / 4πε₀) × (q / r²) directed radially outwards for +q and inwards for -q.
• Properties of Electric Field Lines:
- Start from positive charges and end at negative charges.
- Continuous curves without any breaks in charge-free regions.
- Two field lines never intersect each other (otherwise two directions of E at intersection point).
- Electrostatic field lines do not form closed loops.
4. Electric Dipole & Torque in Uniform Field
Short Note:
• Electric Dipole: A pair of equal and opposite point charges (+q and -q) separated by a distance 2a.
• Dipole Moment (p): Vector quantity directed from negative to positive charge: p = q × 2a. SI unit is C·m.
• Electric Field of Dipole:
- Axial Line (r >> a): E_axial = (1 / 4πε₀) × (2p / r³)
- Equatorial Line (r >> a): E_eq = (1 / 4πε₀) × (p / r³)
• Torque on Dipole in Uniform Field: τ = p × E or τ = pE sin θ. Potential energy stored is U = -p · E = -pE cos θ.
5. Electric Flux & Gauss's Law Applications
Short Note:
• Electric Flux (Φ): Total number of electric field lines passing normally through a given area: Φ = ∫ E · dA = E A cos θ. SI unit is N·m²/C or V·m.
• Gauss's Law: The total electric flux through any closed surface is equal to 1/ε₀ times the total net charge enclosed by the surface: Φ = ∮ E · dA = q_enclosed / ε₀.
• Applications of Gauss's Law:
- Infinitely Long Straight Wire (linear charge density λ): E = λ / (2πε₀r)
- Infinite Plane Sheet (surface charge density σ): E = σ / (2ε₀)
- Thin Spherical Shell (radius R, charge Q): E_out = Q / (4πε₀r²) (for r ≥ R) and E_in = 0 (for r < R).
Intext & Conceptual Questions
If two electric field lines cross each other at a point, it would mean that at the point of intersection, two tangents can be drawn. This implies two different directions for the net electric field at the exact same location, which is physically impossible. Hence, two electric field lines can never cross each other.
• Stable Equilibrium: Dipole moment p is parallel to electric field E (θ = 0°).
- Torque: τ = pE sin 0° = 0
- Potential Energy: U = -pE cos 0° = -pE (Minimum PE)
• Unstable Equilibrium: Dipole moment p is antiparallel to electric field E (θ = 180°).
- Torque: τ = pE sin 180° = 0
- Potential Energy: U = -pE cos 180° = +pE (Maximum PE)
Textbook Chapter End Exercise Questions
Given:
• q₁ = 2 × 10⁻⁷ C
• q₂ = 3 × 10⁻⁷ C
• r = 30 cm = 0.3 m
• k = 1 / (4πε₀) = 9 × 10⁹ N·m²/C²
Using Coulomb's Law formula:
F = k × (|q₁ q₂| / r²)
F = (9 × 10⁹ × 2 × 10⁻⁷ × 3 × 10⁻⁷) / (0.3)²
F = (54 × 10⁻⁵) / 0.09 = 6 × 10⁻³ N
Since both charges are positive, the force is repulsive in nature.
| Feature | Point Charge Electric Field | Electric Dipole Field |
|---|---|---|
| Distance Dependency | E is inversely proportional to r² (E ∝ 1/r²). | E is inversely proportional to r³ (E ∝ 1/r³) at large distances. |
| Symmetry | Spherical symmetry around the charge. | Axial symmetry about the dipole axis. |
| Net Charge | Net charge is non-zero (q ≠ 0). | Net charge is zero (q_total = +q - q = 0). |
Read More & Chapter Resources
These short notes are designed for quick revision. Read the main points once, then use the related material below to practise the same chapter. Revising a concept and checking it with questions can make your preparation more focused.