Electric charges and fields

Chapter One: ELECTRIC CHARGES AND FIELDS

1.1 Introduction

  • Static Electricity: Observations include sparks or crackles when removing synthetic clothes in dry weather or lightning during thunderstorms.

  • Electric Shock: Caused by the discharge of accumulated charges in the body, generated by rubbing insulating surfaces.

  • Electrostatics: Study of forces, fields, and potentials arising from static charges.

1.2 Electric Charge

  • Historical Discovery: Thales of Miletus (circa 600 BC) noted that amber attracts light objects when rubbed with wool or silk.

  • Charge Types: There are two kinds of charges:

    1. Like charges repel.

    2. Unlike charges attract.

  • Polarity of Charge: Glass rod rubbed with silk acquires a positive charge; silk acquires a negative charge.

  • Neutralization: When charged objects come into contact, they neutralize each other.

  • Naming Conventions: Positive charge for glass/ fur; negative for plastic/ silk.

1.3 Conductors and Insulators

  • Conductors: Materials that allow charge passage easily (e.g., metals, human and animal bodies).

  • Insulators: Materials resisting charge transfer (e.g., plastic, wood).

  • Charge Distribution: Charges spread over the surface in conductors, remain localized in insulators.

1.4 Basic Properties of Electric Charge

1.4.1 Additivity of Charges

  • Charges can be summed algebraically as scalars: total charge = q1 + q2 + ... + qn.

1.4.2 Charge Conservation

  • In isolated systems, charge is neither created nor destroyed.

1.4.3 Quantization of Charge

  • Electric charge is quantized, always an integral multiple of the elementary charge (e).

    • Charge on proton: +e; charge on electron: -e.

1.5 Coulomb’s Law

  • Describes the force between two point charges, inversely proportional to the square of their separation and directly proportional to the product of their magnitudes:

    [ F = k \frac{q_1 q_2}{r^2} ]

  • Coulomb Constant (k): Approximately 9 × 10^9 N m²/C².

1.6 Forces Between Multiple Charges

  • Superposition Principle: The net force on a charge is the vector sum of all forces due to other charges.

1.7 Electric Field

  • Electric Field (E): A field surrounding a charge that exerts a force on other charges.

    • Defined as the force per unit charge at a point in the field.

  • Field Due to Point Charge: [ E = k \frac{q}{r^2} ] (direction depends on the sign of q).

1.8 Electric Field Lines

  • Represented as continuous curves; indicate direction and strength of the electric field (density correlates with strength).

  • Properties:

    1. Lines start from positive charges and end at negative charges.

    2. Field lines do not cross.

    3. Field lines cannot form closed loops.

1.9 Electric Flux

  • Definition: Electric flux ( [ \Phi_E = E \cdot A ]) describes the amount of field passing through an area.