Chapter 1. Fundamentals of Electromagnetism
Recommended Post : 【Physics】 Physics Index
1. Terms
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 [Note:1]
○ 1st. Light emitted from a light source
○ 2nd. Light is reflected from the top scanning surface : Less light is reflected from black text, more from white background
○ 3rd. Reflected light hits the drum surface of the photocopier, losing positive charges
○ 4th. Areas corresponding to black text retain their positive charge
○ 5th. Toner particles (carbon powder) are negatively charged, so stick to positively charged areas due to electrostatics
○ 6th. Drum rotates clockwise, transferring toner powder to paper
② Car Painting
Figure. 3. Principle of Car Painting
○ 1st. Positively charged paint particles sprayed into the air
○ 2nd. Car surface induces a positive charge due to electron loss, attracting paint particles
○ 3rd. Paint particles adhere to car surface due to electrostatic attraction
○ 4th. Paint particles, having the same charge, spread evenly without clumping
③ Electrostatic Precipitators
Figure. 4. Principle of Electrostatic Precipitators
○ 1st. Electrons emitted from discharge electrode
○ 2nd. Released electrons attach to dust emitted from power plants or boilers
○ 3rd. Dust particles collect on electrostatically charged plates
④ Electrostatic Separators
○ Electrostatic Separation and Frictional Charging Separation
Figure. 5. Electrostatic Separation and Frictional Charging Separation [Note:4]
○ Electrostatic Separation via Corona Discharge
Figure. 6. Electrostatic Separation via Corona Discharge [Note:5]
⑷ Application 2: Preventing Electrostatic Damage
① Lightning Rod
○ 1st. Electrons accumulate due to friction between water vapor particles in clouds
○ 2nd. Electrons, being heavy, sink beneath the cloud : The lower region of the cloud is negatively charged
○ 3rd. Ground is positively charged due to induction
○ 4th. Lightning rod has a large surface-to-volume ratio, resulting in high positive charge density
○ 5th. Lightning rod forms a strong electric field, ionizing air and releasing positive charges
○ 6th. 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 [Note:6]
○ 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
○ 1st. Vapor from gasoline or diesel at gas stations can cause fires due to electrostatic discharge
○ 2nd. Contacting the electrostatic prevention pad eliminates polarity on the human body
○ 3rd. 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