Electric Charge & Electric Field – Comprehensive Study Notes

1.1 Electric Charge

• Atomic Theory of Matter

  • All matter is composed of atoms (quantization of matter).

  • Each atom contains:

  • Nucleus: protons (positively charged) + neutrons (neutral).

  • Surrounding electrons (negatively charged).

  • Neutral atom ⇒ equal number of protons and electrons.

  • An atom becomes charged when it gains or loses electrons:

  • Loss of electrons → positively charged (cation).

  • Gain of electrons → negatively charged (anion).

• Two Fundamental Types of Charge

  • Positive (+) and Negative (−).

  • Basic law: Like charges repel, unlike charges attract (illustrated in Fig. 1.2).

• Quantization of Charge

  • Any charge $q$ is an integer multiple of the elementary charge $e$:
    $q = n e, \; n = 1,2,3,\ldots \quad (\text{Eq. 1.1})$

  • $e = 1.6 \times 10^{-19}\,\text{C}$ (magnitude for both electron and proton).

  • Smallest negative unit: $q = -e = -1.6 \times 10^{-19}\,\text{C}$ (electron).

  • Smallest positive unit: $q = +e = +1.6 \times 10^{-19}\,\text{C}$ (proton).

• Example 1 (Removal of electrons)

  • Desired charge: $+2.4\,\mu\text{C} = 2.4 \times 10^{-6}\,\text{C}$.

  • Number of electrons removed:
    $n= \frac{q}{e} = \frac{2.4 \times 10^{-6}}{1.6 \times 10^{-19}} = 1.5 \times 10^{13}\;\text{electrons}$.

• Conservation of Electric Charge

  • Charge can neither be created nor destroyed; the algebraic sum produced in any process is zero.

  • Example: rubbing glass with silk ⇒ electrons transfer to silk; total net charge remains zero.

• Charging by Friction (Insulators)

  • Rubbing transfers electrons between insulating materials.

  • Glass rod + silk: electrons move to silk ⇒ glass becomes $+$, silk $−$.

  • Plastic rod + fur: electrons move to plastic ⇒ plastic $−$, fur $+$.

1.2 Conductors, Semiconductors & Insulators

• Conductors

  • Valence electrons loosely bound; become free electrons.

  • Under electric field, free electrons move easily ⇒ good conduction (metals, saline solutions, plasmas).

  • Can be charged by contact or induction.

• Insulators

  • Electrons tightly bound to nuclei; negligible free charges.

  • Charge resides where placed; charging typically requires friction.

• Semiconductors

  • Intermediate conductivity; properties engineered by doping (Si, Ge, GaAs).

  • Mentioned in objectives though not elaborated further in transcript.

• Atomic-level Picture (Fig. 1.4 & 1.5)

  • Valence electrons are either free (conductors) or bound (insulators).

  • Sufficient external energy can liberate bound electrons.

1.3 Charging by Contact & Induction

• Charging by Contact (Fig. 1.5)

  • Steps:

  1. Bring a charged body (e.g.
     negatively charged plastic rod) into contact with neutral conductor.

  2. Electrons transfer until both bodies reach common potential.

  3. After separation: original rod neutral; conductor acquires net charge of same sign as initial rod.

• Charging by Induction (Fig. 1.6)

  • Non-contact method; exploits charge polarization.

  • Procedure (typical):

  1. Bring charged rod near neutral conductor → induces polarization (electrons shift inside conductor).

  2. Ground the conductor’s far side → electrons flow to Earth (or from Earth) while rod remains nearby.

  3. Remove ground → conductor left with net charge opposite to inducing rod.

  4. Remove rod → excess charge redistributes on conductor.

• Conceptual Q&A Highlights

  1. Comb attracts neutral paper via polarization.

  2. Paper later repelled after touching comb because it acquires same sign charge.

  3. Repulsion ⇒ suspended object must carry charge of same sign (cannot be explained by polarization alone).

  4. Attraction does not prove charging; could be neutral object polarized.

1.4 Coulomb’s Law

• Force Between Two Point Charges
  $F = k \frac{|q<em>1 q</em>2|}{r^2} = \frac{1}{4\pi\varepsilon<em>0}\frac{|q</em>1 q_2|}{r^2} \quad (\text{Eq. 1.2})$

  • k = 8.99 \times 10^9\,\text{N·m}^2/\text{C}^2.

  • \varepsilon_0 = 8.85 \times 10^{-12}\,\text{C}^2/(\text{N·m}^2).

  • Direction:

  • Attractive if charges opposite.

  • Repulsive if charges same.

  • Forces obey Newton’s third law: $\vec F<em>{12} = -\vec F</em>{21}$.

• Charge Symbols (Table 1.1)

  • Electron: $-e$; Proton: $+e$; Neutron: $0$.

• Worked Examples

  1. Example 2: $+1\,\text{C}$ and $-1\,\text{C}$ separated by $1000\,\text{m}$ ⇒ $F = 9.0 \times 10^3\,\text{N}$ (attractive).

  2. Example 3 (linear triple charges)

  • Charges: $q<em>1=-3\,\mu\text{C},\;q</em>2=+5\,\mu\text{C},\;q_3=-4\,\mu\text{C}$.

  • Distances: $r<em>{31}=0.5\,\text{m},\;r</em>{32}=0.2\,\text{m}$.

  • Forces: $F<em>{31}=0.43\,\text{N}$ (left), $F</em>{32}=4.5\,\text{N}$ (right).

  • Net force on $q_3$: $-4.1\,\text{N}$ (−x direction).

  1. Example 4 (2-D vectors)

  • $q<em>1=+8.6\times10^{-5}\,\text{C},\;q</em>2=-5.0\times10^{-5}\,\text{C},\;q_3=-6.5\times10^{-5}\,\text{C}$.

  • Distances: $r<em>{31}=0.60\,\text{m},\;r</em>{32}=0.30\,\text{m}$.

  • Components: $F<em>{31x}=120\,\text{N},\;F</em>{31y}=70\,\text{N},\;F_{32y}=325\,\text{N}$.

  • Net components: $F<em>x=120\,\text{N},\;F</em>y=282\,\text{N}$.

  • Magnitude & direction: $F = 290\,\text{N},\;\theta = 65^{\circ}$ above +x axis.

1.5 Electric Field

• Definition

  • Region where a charge experiences electric force.

  • Quantitatively: $\vec E = \frac{\vec F}{q_0}\quad (\text{Eq. 1.3})$.

  • For point charge $q$ at distance $r$:
    $E = k\frac{|q|}{r^2}\quad (\text{Eq. 1.4})$.

  • Units: $1\,\text{N/C} = 1\,\text{V/m}$.

• Direction

  • Direction of force on a positive test charge.

  • Field lines:

  • Originate on $+$ charges, terminate on $-$ charges.

  • Density ∝ magnitude.

  • Never intersect, tangent gives $\vec E$ direction.

  • Configurations illustrated:

  • Isolated point charge (radial).

  • Electric dipole (two opposite charges).

  • Uniform field (parallel plates).

• Worked Examples

  1. Example 5 (single negative charge)

  • $q=-3.0\times10^{-6}\,\text{C},\;r=0.30\,\text{m}$.

  • $E = 3.0 \times 10^{5}\,\text{N/C}$ toward the charge (−x).

  1. Example 6 (two charges, electron at P)

  • Charges: $q<em>1=-25\,\mu\text{C},\;q</em>2=+50\,\mu\text{C}$ separated by $10\,\text{cm}$.

  • Point P: $2\,\text{cm}$ from $q<em>1$, $8\,\text{cm}$ from $q</em>2$.

  • Net field: $E_{net}=6.3\times10^{8}\,\text{N/C}$ in −x direction.

  • Electron acceleration:
    $a = \frac{eE}{m_e} = \frac{1.6\times10^{-19}\,\text{C}\;\cdot\;6.3\times10^{8}\,\text{N/C}}{9.1\times10^{-31}\,\text{kg}} = 1.1\times10^{20}\,\text{m/s}^2$ toward +x (opposite field direction for electron).

  1. Example 7 (symmetrical pair on y-axis)

  • $q<em>1=-4.0\,\mu\text{C},\;q</em>2=+4.0\,\mu\text{C}$ located symmetrically $0.700\,\text{m}$ above/below P on x-axis.

  • Horizontal components cancel; vertical add.

  • Field at P: $E_{net}=7.56\times10^{4}\,\text{N/C}$ along +y.

  • Object: $q_0=+8.0\,\mu\text{C},\;m=1.20\,\text{g}$.

    • $a=\frac{q_0E}{m}=5.04\times10^{2}\,\text{m/s}^2$ along +y.

Ethical, Philosophical & Practical Notes

• Conservation of charge underscores fundamental symmetry and invariance in physics.

• Induction enables non-contact charging, important in electrostatic shielding and sensitive electronics.

• Large electrostatic forces (Coulomb’s law) reveal why matter is stable (attractive forces at atomic scale) yet macroscopic neutral bodies exhibit negligible net charge.

• Uniform field concept crucial for capacitor design (energy storage, filtering, sensors).

• Understanding of conductors/insulators forms basis for electrical safety (grounding, insulation) and semiconductor technology (diodes, transistors).

Numerical / Constant Reference Sheet

• Elementary charge: $e = 1.602\times10^{-19}\,\text{C}$.

• Coulomb constant: k = 8.99\times10^{9}\,\text{N·m}^2/\text{C}^2.

• Permittivity of free space: \varepsilon_0 = 8.85\times10^{-12}\,\text{C}^2/(\text{N·m}^2).

• Electron mass: $m_e = 9.11\times10^{-31}\,\text{kg}$.

• Micro-coulomb: $1\,\mu\text{C} = 1\times10^{-6}\,\text{C}$.

Quick Problem-Solving Strategy

• Identify all charges, signs, magnitudes, positions.

• For forces:

  1. Apply Coulomb’s law pairwise.

  2. Treat direction via vector components.

  3. Sum vectors algebraically (superposition).

• For fields:

  1. Treat every charge as source; compute $E_i$ at point of interest.

  2. Use symmetry to simplify.

  3. Superpose: $\vec E<em>{net}=\sum \vec E</em>i$.

• For motion of test charge:
  $\vec F = q\vec E, \; \vec a = \vec F/m$.

End of Chapter 1 Summary

• Electric charge is discrete, conserved, and interacts via Coulomb forces.

• Conductive behavior depends on mobility of valence electrons.

• Bodies can be charged by friction, contact, or induction.

• Coulomb’s law quantitatively describes electrostatic forces; superposition principle applies.

• Electric field provides field-based description; magnitude $E=k|q|/r^2$, direction via test charge method, visualized by field lines.

• These principles underpin all later topics: electric potential, current, circuits, magnetism, EM waves, optics, quantum & atomic physics.