Applied Physics For Engineering III: Modern Physics

Explore Maxwell's equations, the four pillars of classical electromagnetism, linking electric charges and currents to electric and magnetic fields, deriving electromagnetic waves and the nature of light.

Relate the total flux through a closed surface to the enclosed charge via Gauss's law. Use integral and differential forms; epsilon zero and divergence link field to charge density.

Explore Gauss's law for magnetism, showing zero net flux through any closed surface, no magnetic monopoles, and magnetic field lines that form closed loops, with both integral and differential formulations.

Explore Faraday's law of induction, where a changing magnetic field induces EMF in a loop of wire and powers generators and transformers, proportional to rate of change of magnetic flux.

Learn how Ampere's law gains Maxwell's correction via the displacement current, ensuring magnetic field continuity for time-varying electric fields, and how this underpins electromagnetic phenomena and waves.

Explore fundamentals of optics: reflection, refraction with Snell's law, and diffraction. Understand light behavior in mirrors, lenses, prisms, and its wave–particle–ray nature.

Apply Gauss's law for electricity to a hollow sphere, compute enclosed charge from charge density, and derive the electric field using the sphere’s surface area and epsilon0.

Explore the foundations of special relativity, including the postulates and Lorentz transformations, and learn how time dilation and length contraction arise for observers in different inertial frames, with engineering applications.

Explore time dilation and length contraction at relativistic speeds using Lorentz transformations and the Lorentz factor to ensure accurate engineering designs for high-speed systems.

Examine relativistic energy and momentum at high speeds, focusing on rest mass energy, the Lorentz factor, and mass-energy equivalence.

Describe general relativity's view of gravity as space-time curvature influenced by mass and energy, contrasting with newtonian gravity and special relativity.

Explore quantum mechanics in engineering contexts, focusing on wave-particle duality, the uncertainty principle, the double-slit experiment, and wave function collapse during measurement.

Explore Schrödinger's equation and the wave function as the mathematical framework of quantum mechanics, showing how the squared magnitude yields observable probabilities and how measurement collapses the state.

Explore quantum states and the superposition principle in nanoscale systems, where decoherence limits quantum behavior. Demonstrate how qubits, interference, and entanglement empower quantum computing and sensors.

Explore quantum tunneling, where particles cross barriers via a wave-like state, producing probability beyond the barrier and enabling tunnel diodes and stellar fusion, described by exp(-2 gamma a).

Explore how electromagnetism underpins electric motors and inductive charging, applying Faraday's law and Ampere-Maxwell's law to convert energy to motion and enable wireless power transfer.

Fiber optics transmit light signals with minimal loss through total internal reflection. The core’s higher refractive index confines light for data transmission; lasers manipulate light for cutting and medical procedures.

Explore how relativity drives modern technology, detailing time dilation in GPS, gravitational time dilation of satellite clocks, and relativistic effects in high-speed accelerators like the LHC.

Explore quantum mechanics in material science with superconductors and graphene, explaining Cooper pairs, BCS theory, zero resistance, Meissner effect, and graphene's high electron mobility from band structure.

Explore how physics underpins engineering by linking electromagnetism, relativity, and quantum mechanics to practical applications. See that equations are models guiding engineering solutions and revealing physics from chemistry to biology.