Electric Charges and Fields

Chapter One: Electric Charges and Fields

1.1 Introduction

• Observations of electric discharge:

  • Sparks or crackles from synthetic clothing in dry weather.

  • Lightning during thunderstorms.

  • Feeling electric shocks from metallic objects.

• These phenomena result from the discharge of electric charges accumulated due to friction, known as static electricity.

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

1.2 Electric Charge

• Historical background:

  • Thales of Miletus (around 600 BC) discovered that rubbing amber with wool or silk attracted light objects.

  • The term "electricity" comes from the Greek word "ēlektron" (amber).

• Materials that can be electrified through rubbing:

  • Glass rods rubbed with wool or silk repel each other.

  • Plastic rods rubbed with cat’s fur behave similarly, attracting and repelling other materials depending on their charge.

• Two types of electric charge:

  • Positive and Negative Charges

  • Benjamin Franklin named the charges:

    • Glass rod (positive), Cat's fur (negative), Plastic rod (negative), Silk (negative).

  • Observation: When like charges meet, they repel; when unlike charges meet, they attract. Charges neutralize each other when contact occurs.

1.3 Conductors and Insulators

• Conductors:

  • Substances that allow electricity to pass through easily (e.g., metals, human bodies, earth).

  • Charges on conductors distribute evenly over the surface.

• Insulators:

  • Substances that resist electric current (e.g., glass, plastic, wood).

  • Charges remain fixed at their location and do not distribute.

• Illustrations of electrification process involves NYLON or PLASTIC combs.

• Semiconductors:

  • Intermediate behavior between conductors and insulators.

1.4 Basic Properties of Electric Charge

• Types of Charges:

  • Positive and negative; they cancel each other when they meet.

1.4.1 Additivity of Charges

• Total charge in a system is the algebraic sum of individual charges:
  $q_{ ext{total}} = q_1 + q_2 + q_3 + … + q_n$

• Charges are scalar quantities with proper signs accounted for during addition.

1.4.2 Charge Conservation

• No charge is created or destroyed in charging processes, only transferred.

  • In an isolated system, total charge remains constant despite redistribution.

• Example: A neutron decays into a proton and an electron; the total charge remains zero.

1.4.3 Quantization of Charge

• Charges are integral multiples of the fundamental charge (denoted by $e$):
  $q = n e$ where $n$ is an integer.

• Charge on an electron is $-e$ and on a proton is $+e$ with $e = 1.602 imes 10^{-19} C$ .

• Typical units used in electrostatics:

  • Microcoulomb (μC) = $10^{-6} C$ and

  • Millicoulomb (mC) = $10^{-3} C$.

1.5 Coulomb’s Law

• Coulomb’s Law describes the interaction between two point charges: $F = k rac{|q_1 q_2|}{r^2}$ where:

  • $F$ = magnitude of the force between the charges

  • $k$ = Coulomb’s constant, approximately $9.0 × 10^9 ext{N m}^2/ ext{C}^2$

  • $r$ = distance between charges.

• Experimental Basis:

  • Coulomb measured forces between charged spheres using a torsion balance.

  • The relationship is established at macroscopic levels but applies to subatomic levels as well.

1.5.1 Expressing Coulomb's Law in Vector Form

• The force can also be expressed in vector notation considering unit vectors along the charge directions:
  extbf{F}{12} = k rac{q_1 q_2}{r^2} extbf{{r}}{21}

1.6 Forces Between Multiple Charges

• Principle of Superposition:

  • Total force on any charge in the presence of multiple charges is based on vector addition of the individual forces from all other charges.

1.7 Electric Field

• Definition:

  • An electric field $E$ surrounds a charge $Q$, defined as the force per unit charge exerted on a small test charge placed in an electric field:
    $E = rac{F}{q}$

• Electric field due to a point charge $Q$ at distance $r$:
  $E = rac{k |Q|}{r^2}$ directed radially away from $Q$ if charge is positive and towards $Q$ if charge is negative.

1.7.1 Electric Field due to a System of Charges

• Electric fields can be calculated using superposition from each charge in the system.

1.8 Electric Field Lines

• Field lines visually represent the electric field:

  • Denser where the field strength is high.

  • Direction from positive to negative charges.

• Properties:

  1. Continuous without breaks.

  2. Never cross each other.

  3. Begin at positive charges and end at negative ones.

1.9 Electric Flux

• Electric flux (Φ) through an area $A$ is defined as:
  $ext{Φ} = E imes A imes ext{cos}( heta)$
  where $heta$ is the angle between the electric field and normal to the surface.

1.10 Electric Dipole

• Definition: An electric dipole consists of two equal and opposite charges separated by a distance $2a$:
  $p = q imes 2a ext{ (dipole moment)}$

• Electric field due to a dipole describes its strength and direction.

Summary of Concepts

• Characteristics of electric charge include quantization, conservation, and additivity.

• Coulomb's law describes the interaction between point charges and can be applied using the superposition principle for multiple charges.

• Electric fields can be calculated for discrete and continuous charge distributions and are visually represented by electric field lines, which are characterized by several fundamental properties.

Exercises

1. Problems involving electric forces, electric fields, and electric dipoles to enhance understanding and calculation skills within electrostatics.