PHY 1020 – Electricity & Magnetism Comprehensive Notes

Fundamental Forces

• Four interactions underpin all electrical and magnetic phenomena discussed later.
  • Strong (Color) Force
  • Binds nucleons into atomic nuclei.
  • Carrier: gluons (massless, spin $1$).
  • Effective range $\approx 10^{-15}\,\text{m}$ (nuclear diameter).
  • Relative strength (to electromagnetic) varies with separation; $\sim 25$ at $3\times10^{-17}\,\text{m}$.
  • Electromagnetic Force
  • Governs electricity, magnetism, chemistry, optics.
  • Carrier: photon (mass $0$, spin $1$).
  • Infinite range; falls as $1/r^{2}$.
  • Weak Force
  • Produces beta decay, neutrino interactions.
  • Carriers: $W^+,\,W^- ,\,Z^0$ (masses > 80\,\text{GeV}, spin $1$).
  • Range $\approx 10^{-18}\,\text{m}$ (0.1 % proton diameter).
  • Gravitational Force
  • Acts on mass–energy; carrier (hypothetical) graviton (massless, spin $2$).
  • Infinite range; relative strength $\sim 10^{-41}$ for two protons.
• "Residual Strong" interaction binds nucleons; not applicable to free quarks.

Electric Charge

• Fundamental, indivisible property analogous to mass.
• Two kinds: positive and negative.
• Electrically neutral object: algebraic sum of charges $=0$.
• Conservation of charge: total charge in an isolated system remains constant.
• Quantization
  • Smallest unit: electron/proton magnitude $e = 1.6\times10^{-19}\,\text{C}$.
  • Permittivity of free space: $\varepsilon_0 = 8.854\times10^{-12}\,\text{F\,m}^{-1}$.
• Force/energy language
  • Charge experiences force in presence of other charge or a field; foundational for electricity & magnetism.

Static Electricity & Electric Shocks

• Static discharge voltages: $10^{3}\text{–}10^{5}\,\text{V}$ (felt as “zap”).
• Current involved tiny: $\sim 1\,\text{mA}$ ⇒ power $P = VI \approx 0.001\,\text{A} \times 10^{4}\,\text{V} = 10\,\text{W}$ or less, so usually harmless.

Electric Current, Voltage & Resistance

• Current (I): rate of charge flow $I = \frac{\Delta Q}{\Delta t}$ (ampere = coulomb/second).
• Voltage (V): electric potential energy per unit charge $\text{Volt} = \text{Joule}/\text{Coulomb}$.
  • Energy of one electron at 1 V: $(1\,\text{eV}) = 1.6\times10^{-19}\,\text{J}$.
• Resistance (R): opposition to current; $R = \frac{V}{I}$ (ohm).
• Ohm’s law bundles the three: $V = IR$.

Electricity & Household Power

• Electricity = macroscopic flow of charge; basis for power grids, appliances, lightning.
• Typical North-American service: $110\,\text{V}$ up to $100\,\text{A}$.
  • Maximum household power: $P = VI = (110)(100) = 1.1\times10^{4}\,\text{W}$.
  • 110 W light-bulb draws $I = \frac{110\,\text{W}}{110\,\text{V}} = 1\,\text{A}$.
• Europe: $220\,\text{V}$ ⇒ same power at half current; more efficient but more dangerous touch voltage.

Direct Current (DC) vs Alternating Current (AC)

• DC: charge flows one direction; constant voltage; inefficient for long-distance high-voltage transmission.
  • Sources: batteries, fuel cells, solar panels.
• AC: charge oscillates; transformers raise/lower voltage efficiently; dominant for grid distribution.
  • Frequency (U.S.): 60 Hz; (EU): 50 Hz.
• Historical “War of Currents”
  • Edison (DC, “Wizard of Menlo Park”) vs Tesla (AC, “Wizard of the West”).
  • Notable episodes:
  • Edison allegedly promised Tesla a bonus to improve DC generators, then refused payment.
  • Edison staged public electrocution of an elephant (Topsy) with 6,600 V AC to portray danger.
  • 1915 Nobel Prize rumor: both declined/shared ⇒ neither awarded.
  • 2007: Con Edison ended remaining DC service (begun 1882), cementing AC victory.
• Practical endpoint: grids use AC; DC largely confined to on-board battery electronics or specialized HVDC lines.

Circuit Protection: Fuses & Breakers

• Circuits rated for specific $V$ & $I$.
• Excess current ⇒ resistive heating $P = I^{2}R$ can burn components, start fires.
• Fuse melts or breaker trips to interrupt flow.

Electrical Grid Architecture

• U.S. divided into three major interconnections: Eastern, Western, Texas (ERCOT).
• Grid delivers power through high-voltage lines, substations, local distribution.

Power Loss & High-Voltage Transmission

• Resistive line loss: $P_{\text{loss}} = I^{2}R$.
  • Example: $I = 300\,\text{A},\; R = 2\,\Omega \Rightarrow P_{\text{loss}} = (300)^{2}(2) = 1.8\times10^{5}\,\text{W} = 180\,\text{kW}$.
• Strategy: transmit at high voltage, low current to minimize $I^{2}R$ losses.

Lightning

• Natural high-power discharge.
  • Voltage $\sim 10^{7}\,\text{V}$ (10 MV).
  • Current $\sim 10^{5}\,\text{A}$ (100 kA).
  • Power: $P = VI = (10^{7})(10^{5}) = 10^{12}\,\text{W}$ (terawatt scale, but for microseconds).

Magnetism Basics

• Magnetism arises from moving charge; at atomic scale from electron spin and orbital motion.
• Every magnet has two poles: north and south.
  • Like poles repel; unlike poles attract (analogy to charge but always dipolar).
• Magnetic field lines emerge from north, enter south (by definition of pole orientation).

Permanent, Para- & Ferromagnets

• Ferromagnets: atoms (Fe, Co, Ni, rare earths) have unpaired spins that align in domains, yielding permanent magnets.
• Paramagnets: materials (e.g., fridge steel when cooled) magnetize weakly only in external field.
• Curie Temperature: threshold above which thermal agitation destroys long-range alignment and magnetism.
• Rare-earth magnets (NdFeB, SmCo): more outer-shell electrons ⇒ stronger fields; used in earbuds, hard drives, MRI.
• Magnetic monopoles?
  • Theoretically posited (Grand Unified Theories), but never observed in nature; magnets remain dipoles.

Electromagnets & Fields

• Current-carrying wire generates concentric magnetic field $\mathbf{B}$ (right-hand rule).
• Solenoid or coil + iron core dramatically strengthens field; basis for relays, MRI, maglev.

Earth as a Giant Electromagnet

• Geodynamo: molten iron alloy in outer core + planet’s rotation ⇒ circulating currents ⇒ magnetic field.
• Axis tilted $\approx 11.5^{\circ}$ from geographic rotation axis.
• Earth’s "North Magnetic Pole" is actually a south pole (compass north pole seeks it).
• Field shields planet from solar wind, guiding charged particles to poles (aurorae).
• Einstein considered origin of Earth’s magnetism a major unsolved problem of his era.

Transformers

• Two coils (primary, secondary) linked by common magnetic core.
• Turns ratio $a = N<em>p/N</em>s$ sets voltage ratio: $V<em>s = V</em>p / a$ (for step-down; step-up if a<1).
  • Example: $V<em>p = 1.1\times10^{5}\,\text{V},\; N</em>p = 10{,}000,\; N_s = 10$.
  • $a = 10{,}000/10 = 1{,}000$.
  • $V_s = \frac{1.1\times10^{5}}{1{,}000} = 110\,\text{V}$ (household level).
• Key for efficient AC transmission & device chargers.

Electric Motors

• Current in coil within magnetic field experiences force $\mathbf{F}=I\,\mathbf{L}\times\mathbf{B}$ ⇒ torque.
• Commutator reverses current every half-turn so torque continues same direction (DC motor).
• Brushes deliver current; inefficiencies include friction & arcing.

Electric Generators

• Reverse of motor: mechanical work rotates coil in magnetic field ⇒ induces emf (Faraday’s law).
• Dynamo: outputs DC (using commutator).
• Alternator: outputs AC (slip rings; easier, lower maintenance, basis for modern power plants & cars).

Magnetic Recording & Data Storage

• Dipole orientation (up/down) encodes binary 1/0.
• Used in tapes, hard-disk platters; write head magnetizes tiny domains, read head senses orientation.
• Video reference: YouTube link illustrates microscopic flips.

Eddy Currents

• Changing magnetic flux in conductor induces circulating currents (Lenz’s law).
• Results: energy loss as heat, magnetic damping (drop a magnet through copper pipe slows fall).
• Engineers laminate transformer cores or use ferrites to reduce eddy losses.

Superconductors

• Certain materials exhibit $R \rightarrow 0$ below critical temperature $T_c$.
  • Conventional (NbTi, Nb$3$Sn): $T</em>c\sim 10\text{–}20\,\text{K}$.
  • High-temperature cuprates (YBa$2$Cu$3$O${7-x}$ etc.): Tc > 90\,\text{K} (liquid-nitrogen coolant).
  • Pressure-induced and iron-pnictide examples push $T_c$ higher.
• Plot (transcript) charts evolution of $T_c$ vs discovery year—from Hg (1911) to cuprates & Fe-As.
• Superconductivity allows:
  • Persistent currents without power input.
  • Extremely strong electromagnets (MRI, tokamaks).
  • Quantum levitation (Meissner effect).

Magnetic Levitation (Maglev)

• Superconducting magnets + guiding coils create repulsive forces that lift and propel vehicles.
• Advantages: minimal friction --> high speed, low maintenance.
• Also demonstrated in classroom with superconducting puck floating above magnetic track.