Chapter One: Electric Charges and Fields

1.1 Introduction

• Static Electricity: Observed in instances like synthetic clothes, car doors, and bus iron bars.
• Electrostatics: Study of forces, fields, and potentials from static charges.
• Electric Discharge: Seen in lightning and static shocks.

1.2 Electric Charge

• Historical Discovery: Thales of Miletus (600 BC) observed attraction by amber rubbed with wool.
• Charge Types: Defined as positive and negative by Benjamin Franklin.
• Behavior:
  • Like charges repel, unlike charges attract.
  • Charges neutralize each other on contact.
• Electrification: Rubbing materials causes charge transfer.
• Gold-leaf Electroscope: Detects charge on bodies.
• Nature of Charges:
  • Charges arise from electron transfer.
  • Conductors allow electron flow; insulators do not.

1.3 Conductors and Insulators

• Conductors: Allow electricity to pass; metals, human bodies.
• Insulators: Resist electricity; glass, plastic.
• Semiconductors: Intermediate resistance.

1.4 Basic Properties of Electric Charge

1.4.1 Additivity of Charges

• Total charge is algebraic sum of individual charges.

1.4.2 Charge is Conserved

• Charge transfer does not create/destroy charges.

1.4.3 Quantisation of Charge

• Charge is an integral multiple of the elementary charge e.

1.5 Coulomb's Law

• Force Between Charges:
  • Proportional to product of charges and inversely to the square of distance.
  • Constants: k ~ 9 \times 10^9 Nm^2/C^2.
• Torsion Balance: Used by Coulomb to measure force.
• Coulomb’s Law Vector Form: Used for point charges.

1.6 Forces Between Multiple Charges

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

1.7 Electric Field

• Field Concept: Charge creates a field affecting other charges.
• Electric Field Definition: Force per unit charge.
• Directionality:
  • Field from positive charge is outward.
  • Field from negative charge is inward.

1.7.1 Electric Field Due to a System of Charges

• Superposition Principle: Field is vector sum of individual fields.

1.7.2 Physical Significance

• Field as an Intermediate Quantity: Useful in dynamic electromagnetic phenomena.

1.8 Electric Field Lines

• Field Line Properties:
  • Start/stop at charges or infinity.
  • Density indicates field strength.
  • Cannot cross each other.

1.9 Electric Flux

• Definition: Measure of field lines through a surface.
• Dependence: On orientation and area size.

1.10 Electric Dipole

• Definition: A pair of equal and opposite charges.
• Dipole Moment: Product of charge and separation.
• Field: Falls off faster than that of a single charge.

1.10.1 Field of an Electric Dipole

• Axis and Equatorial Plane: Field calculated differently for each.

1.10.2 Physical Significance

• Polar Molecules: Permanent dipoles like water.

1.11 Dipole in a Uniform External Field

• Torque: Aligns dipole with the field.
• Non-uniform Field: Exerts net force.

1.12 Continuous Charge Distribution

• Charge Density Concepts:
  • Surface, line, and volume charge densities.

1.13 Gauss’s Law

• Flux through a Surface: Total charge enclosed divided by permittivity.
• Applications: Simplifies field calculations for symmetric distributions.

1.14 Applications of Gauss's Law

1.14.1 Infinite Line Charge

• Field: Radially outward/inward depending on charge sign.

1.14.2 Infinite Plane Sheet

• Field: Perpendicular to the sheet.

1.14.3 Spherical Shell

• Inside Field: Zero.
• Outside Field: As if charge at center.

Summary

• Electric Forces: Govern atomic and molecular structures.
• Charge Properties: Quantisation, additivity, and conservation.
• Coulomb’s Law and Electric Field: Central to electrostatics.
• Gauss's Law: Useful for symmetric charge distributions.

Exercises

• Problems on charges, electric field calculations, Gauss's law applications, etc.