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Chapter 1. Fundamentals of Electromagnetism

Recommended Post: 【Physics】 Physics Index

1. Terms

2. Static Electricity

3. Law of Charge Conservation

4. Maxwell’s Equations

1. Terms

⑴ Charge

① Definition: Fundamental property that causes electric phenomena

② Types of Charge: Positive and negative charges; like charges repel, unlike charges attract

③ Charge Quantity: Measurement of charge’s magnitude

○ Unit: Coulomb (C)

○ Charge of 1 Electron = -1.6 × 10^-19 C

○ Number of Electrons in 1 C = 6.25 × 10^18

○ Coulomb’s definition and Avogadro’s number (6.02 × 10^23) are unrelated

○ Charge of 1 mol of Electrons = (6.02 × 10^23) × (1.6 × 10^-19) = 96,485 C

○ Since the elementary charge is very small, we consider charge quantities continuously

④ Copper at 20 ℃ has an electron density of 10^23 electrons/cm^3

⑤ Separation of charges causes voltage, and the flow of charges causes current

⑵ Electric Current

① Definition: Net flow of charged particles per unit time

○ Conductors: Allow free electrons to flow, resulting in current

○ Electrolytes: Allow ion flow, leading to current

○ Vacuum Tubes: Positive ions and electrons create current flow

○ Unit: C/s = Ampere (A)

② Current Direction

○ Movement of charges: Electrons move when a force is applied, nuclei remain stationary

○ Current Direction: (+) to (-)

○ Movement of Free Electrons: (-) to (+)

○ Movement of Positive Charges: (+) to (-)

③ Type 1: Drift Current

○ Definition: Movement of free electrons in conductors due to electric field

○ Electrons have higher mobility than positive charges

○ Ohm’s law applies only to drift current

○ Application: FET Transistors

④ Type 2: Convection Current (Diffusion Current)

○ Definition: Movement of charged particles through convection or diffusion

○ Examples: Vacuum tubes, rarefied gases

○ Application: PN Junction Diodes, BJT Transistors

⑤ Type 3: Polarizing Current: Time-dependent polarization

⑥ Type 4: Displacement Current: Time-dependent change in charge density, hypothetical current

⑶ Electric Potential

① Electric Field: Magnitude of electric force per unit charge

② Electric Potential: Electric potential energy per unit charge

③ Voltage: Energy required to separate charges per unit charge (Unit: Joule/Coulomb = Volt)

④ Electric field and potential in regions with constant electric field

⑤ Electric field from potential-distance graph corresponds to the slope of the tangent

⑷ Power: Rate of doing work by an electrical device, 1 Horsepower (hp) = 735 W

① Power in Resistors

② Power in Electric Motors

③ Sign of Power

○ Positive value: Energy transferred to circuit component

○ Negative value: Energy dissipated from circuit component

④ Tip: Power in resistors is always positive

○ Positive power when current flows, negative power when it doesn’t

○ Note: The sign is conventional, not indicative of reality

Figure 1. Rule for power signs in resistors

⑤ Sum of powers in any circuit is 0 due to conservation of energy

⑸ Electric Field Lines

① Electric Field Lines: Curves showing direction of electric field of a positive unit charge

② Equipotential Surface: Surface connecting points with equal electric potential

③ Following electric field lines leads to decrease in electric potential

④ Electric field lines and equipotential surfaces are perpendicular

⑹ Magnetic Field Lines

2. Static Electricity

⑴ Overview

① Electrification: Phenomenon of objects acquiring charge

② Charged Object: Object with acquired charge

③ Triboelectric Series: Ranking of materials based on their tendency to become charged when rubbed together

(+) Fur → Glass → Silk → Wood → Cotton → Rubber → Plastic → Ebonite (-)

④ Conductors do not hold static charge: Charges distribute evenly without accumulation

⑵ Electrostatic Induction

① Frictional Charging: Transfer of electrons between objects in contact

② Electrostatic Induction: Movement of electrons within an object

⑶ Application 1: Utilizing Electrostatic Induction

① Photocopiers and Printers

Figure 2. Principle of Photocopiers and Printers

○ 1^st. Light emitted from a light source

○ 2^nd. Light is reflected from the top scanning surface: Less light is reflected from black text, more from white background

○ 3^rd. Reflected light hits the drum surface of the photocopier, losing positive charges

○ 4^th. Areas corresponding to black text retain their positive charge

○ 5^th. Toner particles (carbon powder) are negatively charged, so stick to positively charged areas due to electrostatics

○ 6^th. Drum rotates clockwise, transferring toner powder to paper

② Car Painting

Figure 3. Principle of Car Painting

○ 1^st. Positively charged paint particles sprayed into the air

○ 2^nd. Car surface induces a positive charge due to electron loss, attracting paint particles

○ 3^rd. Paint particles adhere to car surface due to electrostatic attraction

○ 4^th. Paint particles, having the same charge, spread evenly without clumping

③ Electrostatic Precipitators

Figure 4. Principle of Electrostatic Precipitators

○ 1^st. Electrons emitted from discharge electrode

○ 2^nd. Released electrons attach to dust emitted from power plants or boilers

○ 3^rd. Dust particles collect on electrostatically charged plates

④ Electrostatic Separators

○ Electrostatic Separation and Frictional Charging Separation

Figure 5. Electrostatic Separation and Frictional Charging Separation

○ Electrostatic Separation via Corona Discharge

Figure 6. Electrostatic Separation via Corona Discharge

⑷ Application 2: Preventing Electrostatic Damage

① Lightning Rod

○ 1^st. Electrons accumulate due to friction between water vapor particles in clouds

○ 2^nd. Electrons, being heavy, sink beneath the cloud: The lower region of the cloud is negatively charged

○ 3^rd. Ground is positively charged due to induction

○ 4^th. Lightning rod has a large surface-to-volume ratio, resulting in high positive charge density

○ 5^th. Lightning rod forms a strong electric field, ionizing air and releasing positive charges

○ 6^th. Lightning is attracted to the lightning rod

○ Reason for high positive charge density on the lightning rod

Figure 7. Reason for High Positive Charge Density on the Lightning Rod

○ Charge can move freely on the surfaces of the two conductor spheres

○ Charge movement continues until the potentials on the surfaces of the conductor spheres are equal

○ Reason: If there’s a potential difference, a force arises

○ Electric field on the conductor sphere surface is greater with smaller sphere radius

② Electrostatic Prevention Pads

Figure 8. Electrostatic Prevention Pads

○ 1^st. Vapor from gasoline or diesel at gas stations can cause fires due to electrostatic discharge

○ 2^nd. Contacting the electrostatic prevention pad eliminates polarity on the human body

○ 3^rd. Human-induced electrostatic charges are minimized, reducing fire risks

3. Law of Charge Conservation: Continuity equation of charge

⑴ Definition: Charge is neither created nor destroyed

⑵ Mathematical Expression: Utilizes divergence theorem

⑶ Physical Interpretation

① Related to definition of current

② Total charge in the universe is 0

4. Maxwell’s Equations

⑴ Law 1: Gauss’s Law for Electricity

① Definition: Electric field is generated by charges

○ Circuit Theory relates to Gauss’s Law for Electricity

② Mathematical Expression: Utilizes divergence theorem

○ D represents electric flux density

○ Integral of electric field along a Gaussian surface equals charge divided by permittivity

③ Example 1: Electric field and potential at distance r from a point charge q (Coulomb’s Law)

④ Example 2: Electric field and potential due to a line charge density λ (C/m) in an infinitely long charged conductor

⑤ Example 3: Electric field and potential due to a surface charge density σ (C/m^2) on an infinitely charged plane conductor

⑵ Law 2: Gauss’s Law for Magnetism

① Definition: No magnetic monopoles exist

② Mathematical Expression

③ μH represents magnetic flux density

④ Quantum mechanically, magnetic monopoles are possible: Hypothesized in the early universe

⑶ Law 3: Ampère’s Circuital Law

① Definition: Currents create magnetic fields

② Mathematical Expression: Utilizes Green’s theorem

○ In vacuum or air, B and H are linearly related

○ Generally expressed in terms of magnetic field

③ Physical Interpretation

○ Magnetic field is generated around space with current or virtual current

○ Magnetic field’s direction follows the right-hand screw rule

⑷ Law 4: Faraday’s Law of Electromagnetic Induction

① Definition: A changing magnetic field induces a current

② Mathematical Expression: Utilizes Green’s theorem

③ Physical Interpretation: Changing magnetic flux through an arbitrary surface induces current along the surface’s boundary

⑸ Derivation of Wave Equations

① Problem scenario (To be updated later)

② Utilization of Faraday’s Law

③ Utilization of Ampère’s Circuital Law

④ Derivation of wave equations: Can deduce speed of light

Input: 2019-07-07 18:57