Electric Charges and Fields Notes

Chapter One: Electric Charges and Fields

1.1 Introduction

• Static Electricity: Occurs from the accumulation of electric charges, leading to observable phenomena like sparks or lightning.
• Electrostatics: The study of forces, fields, and potentials arising from static charges.

1.2 Electric Charge

• Historical Background:
  • Thales of Miletus discovered that amber attracted light objects when rubbed.
  • The term 'electricity' derives from the Greek word for amber, 'ēlektron'.
• Types of Electric Charges:
  • Positive & Negative: Identified by the behavior of materials rubbed against each other (like charges repel, unlike charges attract).
  • Charge on glass rods rubbed with silk is positive (+) and the charge on plastic rods rubbed with fur is negative (–).
• Charge Neutralization: Bringing like-charged objects into contact neutralizes their charge.

1.3 Conductors and Insulators

• Conductors: Materials that allow electric charges to flow freely (e.g., metals, human body).
• Insulators: Materials that do not allow the flow of electric charges (e.g., rubber, glass).

1.4 Basic Properties of Electric Charge

1. Additivity of Charges: The total charge is the algebraic sum of all individual charges.
   • Example: For charges +1, +2, -3, +4, -5, the total charge = (+1) + (+2) + (-3) + (+4) + (-5) = -1.
2. Conservation of Charge: Charge is neither created nor destroyed but transferred; the total charge in an isolated system remains constant.
3. Quantisation of Charge: All charges are integral multiples of a basic unit of charge, denoted by $e$. A charge can be expressed as:\
   $q = n \cdot e$ where $n$ is an integer.
4. Unit of Charge:
   • SI unit is Coulomb (C), where 1 Coulomb = charge that flows in 1 second at 1 Ampere.
   • Charge on an electron = –e = approximately $-1.6 \times 10^{-19}$ C.

1.5 Coulomb’s Law

• Definition: The force between two point charges is given by:\ $F = k \frac{q<em>1 q</em>2}{r^2}$ where:
  • $F$ = force between the charges,
  • $q1, q2$ = magnitudes of the charges,
  • $r$ = distance between the charges,
  • $k$ = Coulomb's constant = approximately $9 \times 10^9 \text{N m}^2/ ext{C}^2$.
• Experiments: Coulomb measured force using a torsion balance and established the law at both macroscopic and subatomic levels.

1.6 Electric Field

• Definition: Electric field $E$ at a point due to a charge $Q$ is defined as the force per unit charge exerted on a positive test charge placed at that point. The formula is given by:\
  $E = \frac{F}{q}$
• Electric Field Due to Point Charges: The electric field due to a point charge $Q$ at a distance $r$ is given by:\
  $E = \frac{1}{4\pi \varepsilon_0} \frac{Q}{r^2}$
• Positive Charge: Field lines point radially outwards; negative charge, radially inwards.

1.7 Electric Field Due to Multiple Charges

• Superposition Principle: The total field at a point due to multiple charges is the vector sum of the individual fields due to each charge.
  $E<em>{net} = E</em>1 + E<em>2 + … + E</em>n$

1.8 Electric Flux

• Definition: Electric flux ($\PhiE$) through an area $A$ is defined as:\ $\Phi</em>E = E \cdot A$ where $A$ is vector normal to the area.
• Gauss’s Law:
  • Total electric flux through a closed surface is proportional to the charge enclosed:
    $\Phi<em>E = \frac{q</em>{enc}}{\varepsilon_0}$
  • This is useful for calculating the field for symmetric charge distributions.

1.9 Applications of Gauss’s Law

• Gauss's Law simplifies calculating electric fields for symmetric situations:
  • Infinitely long wire: $E = \frac{\lambda}{2\pi \varepsilon_0 r}$
  • Infinitely large plane sheet: $E = \frac{\sigma}{2 \varepsilon_0}$
  • Thin spherical shell: Outside shell, behaves as point charge: $E = \frac{q}{4\pi \varepsilon_0 r^2}$; inside it is zero.

1.10 Summary of Key Concepts

• Electric charges exist as positive and negative; like charges repel and unlike attract.
• Forces between charges follow Coulomb’s law and are mediated via electric fields.
• The principle of superposition applies to both forces and electric fields.