Chapter One: Electric Charges and Fields

1.1 Introduction

• Static electricity experienced during everyday activities (e.g., removing synthetic clothes) is due to electric discharge.
• Electrostatics: Study of forces, fields, and potentials from static charges.

1.2 Electric Charge

• Discovery of electric charge attraction dates back to Thales of Miletus (600 BC).
• Like charges repel; unlike charges attract.
• Polarity of charge: Differentiates positive and negative charges.
• Benjamin Franklin: Named charges as positive (glass rod) and negative (plastic rod).
• Conservation of charge: Charges neutralize upon contact.

1.3 Conductors and Insulators

• Conductors: Allow easy passage of electricity (e.g., metals).
• Insulators: Resist the passage of electricity (e.g., plastic, wood).
• Semiconductors: Intermediate resistance.
• Charge distribution differs between conductors and insulators.

1.4 Basic Properties of Electric Charge

1.4.1 Additivity of Charges

• Charges add up like real numbers; can be positive or negative.
• Total charge in a system is the algebraic sum of individual charges.

1.4.2 Charge is Conserved

• Charge transfer involves electron movement; no creation or destruction of charge.
• Total charge in an isolated system remains constant.

1.4.3 Quantisation of Charge

• Charge is an integral multiple of a basic unit (e), e.g., electrons carry -e.
• Quantisation evident at microscopic levels but negligible macroscopically.

1.5 Coulomb's Law

• Describes force between two point charges: Inversely proportional to the square of the distance.
• Force is repulsive or attractive based on charge signs.
• Introduced by Charles Augustin de Coulomb using a torsion balance.
• Coulomb's constant: k = 9 × 10⁹ Nm²/C²

1.6 Forces Between Multiple Charges

• Superposition principle: Total force is vector sum of individual forces.

1.7 Electric Field

• Electric field: Force per unit charge due to another charge.
• Electric field lines represent force direction on a positive test charge.
• Field direction depends on charge polarity: Outward for positive, inward for negative.

1.8 Electric Field Lines

• Field lines represent electric field direction and strength.
• Density of lines indicates field strength.
• Properties:
  • Continuous without breaks.
  • Never cross each other.
  • Start at positive and end at negative charges.

1.9 Electric Flux

• Electric flux: Measure of the number of field lines passing through an area.
• Flux depends on field strength, area size, and angle between field and area.

1.10 Electric Dipole

• Dipole: Two equal and opposite charges separated by a distance.
• Dipole moment: Product of charge and distance, directed from negative to positive.
• Field decreases with distance faster than a single charge.

1.11 Dipole in a Uniform External Field

• Dipole experiences torque in an external electric field.
• Torque tends to align dipole with the field.

1.12 Continuous Charge Distribution

• Charge distribution can be linear, surface, or volume.
• Charge density: Charge per unit length, area, or volume.

1.13 Gauss's Law

• Total electric flux through a closed surface is proportional to the charge enclosed.
• Useful for calculating electric field with symmetrical charge distributions.

1.14 Applications of Gauss's Law

• Simplifies electric field calculations for:
  • Infinite line charges.
  • Plane sheets of charge.
  • Spherical shells.
• Field outside a shell behaves as if all charge is concentrated at the center.

Summary

• Electric charge properties: Quantized, additive, conserved.
• Coulomb's law and electric field principles are fundamental.
• Gauss's law aids in calculating fields for symmetric distributions.
• Electric dipoles and field lines provide insights into charge interactions.