📘 Chapter 1 : Electric Charges (Class XII)

🔷 1. Introduction

Electric charge is a fundamental property of matter responsible for all electrical phenomena. It is the source of electric forces and fields. Charges exist in two types: positive (+) and negative (-). Like charges repel and unlike charges attract each other.

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🔷 2. Nature of Electric Charge

• Charge is scalar quantity.
• SI unit: Coulomb (C).
• Quantization of charge: Q = ne, where e = 1.6 × 10^-19 C.
• Charge is always conserved.

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🔷 3. Properties of Electric Charge

Electric charge has four fundamental properties:

• Additivity: Total charge is algebraic sum of individual charges.
• Conservation: Charge can neither be created nor destroyed.
• Quantization: Charge exists in discrete packets.
• Invariance: Charge is independent of reference frame.

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🔷 4. Coulomb’s Law

Force between two point charges is directly proportional to product of charges and inversely proportional to square of distance between them.

F = k (q₁q₂ / r²)

Where k = 1 / (4πε₀) = 9 × 10⁹ Nm²/C² in vacuum.

• Force acts along the line joining the charges.
• Repulsive for like charges, attractive for unlike charges.

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🔷 5. Superposition Principle

When multiple charges are present, net force on a charge is vector sum of forces due to all other charges individually.

F_net = F₁ + F₂ + F₃ + ...

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🔷 6. Electric Field

Electric field is region around a charge where another charge experiences force.

E = F / q

For a point charge:

E = kq / r²

• Direction of electric field is outward for + charge and inward for - charge.

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🔷 7. Electric Field Lines

• Start from positive charge and end on negative charge.
• Never intersect each other.
• Density of lines indicates strength of field.
• Always perpendicular to conducting surface.

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🔷 8. Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a small distance.

Dipole moment: p = q × 2a

• Direction of dipole moment is from negative to positive charge.

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🔷 9. Torque on Dipole in Electric Field

τ = pE sinθ

• Dipole aligns itself along the electric field in equilibrium.

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🔷 10. Key Advanced Results (Must Remember)

• Force in medium: F = (1/4πε) (q₁q₂ / r²)
• Permittivity relation: ε = ε₀εr
• Electric field inside conductor: E = 0
• Charge resides on surface of conductor.
• Gauss’s Law (intro idea): Flux depends only on enclosed charge.

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🔷 11. Summary

Electric charges form the foundation of electrostatics. From Coulomb’s law to electric fields and dipoles, all concepts build toward understanding electric flux and Gauss’s law in higher studies. Mastery of these fundamentals is essential for JEE, NEET, and advanced physics.

✨ End of Chapter: Electric Charges ✨