Physics Chapter 16 – Electric Charge and Electric Field

Static Electricity, Electric Charge, and Its Conservation

• Everyday observation: rubbing certain materials (plastic, glass, wool, silk) produces noticeable forces → the phenomenon of static electricity.
  • Experiment 1 (undisturbed plastic rods):
  • No interaction → objects are electrically neutral.
  • Experiment 2 (both plastic or both glass rods rubbed):
  • Like–like interactions (plastic-plastic, glass-glass) → long-range repulsion.
  • Rubbing = charging; charged objects exert new forces.
  • Experiment 3 (rubbed glass vs. rubbed plastic):
  • Opposite materials attract → existence of two distinct charge types.
  • Convention: glass → positive charge, plastic → negative charge.
  • Experiment 4 (vary distance & vigor of rubbing):
  • Force decreases with increasing separation.
  • Force increases with greater amount of charge transferred.
• Fundamental qualitative rules:
  • Like charges repel; opposite charges attract.
  • Electric force can be attractive or repulsive (contrast with always-attractive gravity).
• Conservation of charge:
  • In any process the algebraic sum of all charge is constant; charge can move or redistribute but cannot be created or destroyed.

Atomic Structure of Charge

• Atom model:
  • Dense nucleus: positive protons (+) & neutral neutrons (0).
  • Light electrons (−) form surrounding cloud.
  • Charge is an intrinsic property of electrons and protons; magnitude of elementary charge e = 1.602\times10^{−19}\ \text{C}.
• Charge quantization:
  • Net charge Q is an integer multiple of e.
• Charged matter:
  • Positive objects have lost electrons (not gained protons).
  • Ionization: removing an electron → positive ion; adding an electron → negative ion.
• Polar molecules:
  • Overall neutral but internal charge distribution is asymmetric → permanent electric dipole.
  • Example: \text{H}_2\text{O} — slight + on H side, − on O side.

Conductors, Insulators, and Semiconductors

• Conductor:
  • Electrons are free to move throughout bulk (e.g., metals, electrolytes).
  • Charge placed on a conductor redistributes until electrostatic equilibrium.
• Insulator (non-conductor):
  • Electrons bound; almost no macroscopic charge flow (e.g., glass, rubber, wood).
• Semiconductor: intermediate behavior (e.g., Si, Ge); conductivity can be engineered.

Charging by Conduction and Induction; The Electroscope

• Conduction (contact):
  • Touch a neutral conductor (A) with a charged object (B) → electrons move until potentials equalize → A acquires same-sign charge as B.
• Induction (no contact):
  • Bring charged body near neutral conductor → internal electrons shift (charge separation).
  • Ground the far side → electrons leave/enter → remove ground & charged body → conductor attains opposite sign to inducing charge.
• Electroscope:
  • Metal rod plus gold leaves inside insulating container.
  • Leaves diverge when charged (either by conduction or induction).
  • Using a known-sign charge, can determine sign of an unknown charge by observing attraction/repulsion during test.
• Non-conductors under induction:
  • Cannot transfer charge, but their molecular dipoles re-orient → polarization leads to attractive force toward charged object.

Coulomb’s Law

• Empirical law relating point charges:
  • F = k \frac{|Q1 Q2|}{r^2}
  • F: magnitude of electric force between two point charges.
  • r: center-to-center separation.
  • k = 8.988\times10^{9}\ \text{N·m}^2/\text{C}^2 = \frac{1}{4\pi\varepsilon_0}.
  • Direction: along line joining charges; attractive if Q1 Q2 < 0, repulsive if Q1 Q2 > 0.
• Typical laboratory charges: 1\ \mu\text{C} = 10^{−6}\ \text{C}.

Problem-Solving with Coulomb’s Law and Vectors

• Superposition principle:
  • Net force on any charge = vector sum of individual Coulomb forces from every other charge.
• Vector methods:
  • Tail-to-tip, parallelogram, or component addition Fx = \sum Fi \cos\thetai,\; Fy = \sum Fi \sin\thetai.
• Example (charges −1.0 nC & +4.0 nC, r = 1.0\ \text{cm}):
  • F = k \frac{(1.0\times10^{−9})(4.0\times10^{−9})}{(1.0\times10^{−2})^2} \approx 3.6\times10^{−4}\ \text{N}, direction: attractive (toward each other).

The Electric Field

• Definition: field at point in space equals force per unit positive test charge.
  • \mathbf{E} = \frac{\mathbf{F}}{q_{\text{test}}}
• Field of a single point charge Q:
  • \mathbf{E}(\mathbf{r}) = k \frac{Q}{r^2}\,\hat{r} (radial; outward if Q>0, inward if Q<0).
• Force on charge in known field:
  • \mathbf{F} = q\,\mathbf{E}.
• Superposition for fields:
  • \mathbf{E}{\text{net}} = \sumi \mathbf{E}_i.
• Example 20.7 (field of proton at electron orbit, r=0.053\ \text{nm}):
  • E = k\,\frac{e}{r^2} = 5.1\times10^{11}\ \text{N/C}, radially outward.

Electric Field Lines

• Graphical representation rules:
  1. Lines are tangent to \mathbf{E} direction at every point.
  2. Density of lines ∝ magnitude of field.
  3. Begin on + charges, end on − charges; number of originating/terminating lines ∝ |charge|.
• Special cases:
  • Electric dipole: equal & opposite charges separated by small distance; characteristic pattern curves from positive to negative.
  • Parallel-plate capacitor: between two large, closely spaced, oppositely charged plates lines are parallel & equally spaced → uniform field.

Electric Fields and Conductors

• Electrostatic equilibrium:
  • Inside conductor: \mathbf{E}=0 → no net motion of free electrons.
  • Excess charge resides on outer surface.
  • Field at surface is perpendicular; any tangential component would drive surface currents.
• Shielding (Faraday cage):
  • Enclosing region with conducting shell screens internal volume from external static fields (and vice-versa).
• Charge density non-uniformity:
  • Accumulates at sharp points → large local E; used deliberately (lightning rods) to initiate air ionization and safely bleed charge.

Applications and Biological Connections

• Heart dipole & electrocardiogram (ECG):
  • Depolarization/repolarization waves create a time-varying electric dipole; field extends through torso, measured by surface electrodes to diagnose cardiac function.
• Molecular biology – DNA:
  • Double helix stabilized by electrostatic attraction between complementary nucleotide bases (A–T, G–C).
  • During replication, random thermal motion brings bases together; correct pairs attract electrostatically, guiding accurate copying.
• Photocopy machines & laser printers:
  • Steps:
  1. Drum given uniform positive charge via charging roller.
  2. Optical image (or laser-written pattern) discharges selected areas.
  3. Negatively charged toner particles adhere to remaining + regions.
  4. Paper contacts drum; toner transfers.
  5. Heat/pressure rollers fuse toner permanently.

Gauss’s Law and Electric Flux

• Electric flux through surface element \Delta A at angle \theta from \mathbf{E}:
  • \Delta\Phi_E = \mathbf{E}\cdot\Delta\mathbf{A} = E\,\Delta A \cos\theta.
• Total flux through closed surface:
  • \PhiE = \ointS \mathbf{E}\cdot d\mathbf{A}.
• Gauss’s law:
  • \PhiE = \frac{Q{\text{enc}}}{\varepsilon_0}.
• Useful for highly symmetric charge distributions (spherical, cylindrical, planar) to obtain \mathbf{E} without direct integration.
• Sample numeric exercise: given \PhiE = 5.0\times10^{4}\ \text{N·m}^2/\text{C} through sphere of radius 20 cm → Q{\text{enc}} = \PhiE \varepsilon0 = (5.0\times10^{4})(8.85\times10^{−12}) \approx 4.4\times10^{−7}\ \text{C}.

Chapter-End Key Facts & Equations

• Charge properties:
  • Two kinds (( +, − )), conserved, quantified in units of e.
• Material categories: conductors (mobile e⁻), insulators, semiconductors.
• Charging mechanisms: conduction, induction, polarization.
• Coulomb’s law: F = k \dfrac{Q1 Q2}{r^2}.
• Electric field: \mathbf{E} = \dfrac{\mathbf{F}}{q} = k \dfrac{Q}{r^2}\,\hat{r}.
• Field lines visualization rules (direction, density, origin/termination).
• Conductor equilibrium: \mathbf{E}_{\text{inside}} = 0; excess charge on surface; surface \mathbf{E} perpendicular.
• Electric flux: \Phi_E = \oint\mathbf{E}\cdot d\mathbf{A}.
• Gauss’s law: \PhiE = Q{\text{enc}}/\varepsilon_0.
• Constants:
  • e = 1.602\times10^{−19}\ \text{C}, k = 8.988\times10^{9}\ \text{N·m}^2/\text{C}^2, \varepsilon_0 = 8.854\times10^{−12}\ \text{C}^2/\text{N·m}^2.
• Practical scales: rubbing produces micro-coulomb charges; atomic fields ≈ 10^{11}\ \text{N/C}; everyday copier fields cause toner attraction; biological dipoles drive ECG signals.