Electric Charge & Electric Fields Explained | Chapter 21 of University Physics

Chapter 21 lays the groundwork for understanding electrostatics by exploring how objects acquire charge, how charged particles interact via Coulomb’s law, and how the electric field concept unifies these interactions. This chapter also shows how to visualize fields with field lines and calculate fields for both point charges and continuous charge distributions.

Watch the full video summary on YouTube for step-by-step examples and field visualizations.

Electric Charge & Conservation

Electric charge comes in two types—positive and negative—with like charges repelling and opposites attracting. Protons carry positive charge, electrons negative, and neutrons are neutral. The conservation of charge principle states that the total charge in a closed system remains constant, meaning charge can be transferred but never created or destroyed.

Charging by Friction, Polarization & Induction

Objects become charged through:

• Triboelectric effect (friction): rubbing materials transfers electrons.
• Polarization: a neutral object’s charges separate when near a charged body.
• Induction: bringing a charged object close and grounding allows net charge transfer without direct contact.

Coulomb’s Law & Electrostatic Force

Coulomb’s Law quantifies the force between two point charges:

F = k · |q₁ q₂| / r²,

where k ≈ 8.99×10⁹ N·m²/C² and the force acts along the line connecting the charges. It is attractive for opposite signs and repulsive for like signs. By the superposition principle, the net force on a charge is the vector sum of forces from all other charges.

Electric Field Concept

The electric field E at a point is defined as the force per unit test charge:

E = F / q₀.

For a point charge:

E = (1 / 4πε₀) · (q / r²) · r̂,

where ε₀ = 8.85×10⁻¹² C²/N·m². Field lines visualize the field: they emanate outward from positive charges, inward toward negatives, never cross, and their density indicates field strength.

Fields from Discrete & Continuous Distributions

To find the field from multiple charges, sum the individual fields vectorially. For continuous charge distributions, integrate contributions:

• Linear density λ = dQ/dL for wires.
• Surface density σ = dQ/dA for sheets.
• Volume density ρ = dQ/dV for solids.

Examples include:

• Ring of charge: field on axis via ∫dE contributions.
• Disk: treat as concentric rings.
• Infinite plane: uniform field perpendicular to surface.

Electric Dipoles

An electric dipole consists of equal and opposite charges separated by distance d. Its dipole moment is p = q·d (from – to +). In an external field, the dipole experiences a torque:

τ = p × E = p E sinθ,

and has potential energy U = –p · E = –p E cosθ. Dipole fields fall off as 1/r³ at large distances.

Conclusion

Electric charge and field concepts form the foundation of electromagnetism. By mastering Coulomb’s Law, field visualization, and superposition—including continuous distributions and dipoles—you’ll be prepared for advanced topics like Gauss’s Law and electric potential.

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