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4.11. Electromagnetism (ELM)
Electromagnetism studies the behavior of electric charges at rest and in motion, the properties of electric and magnetic fields, and their interaction as described by Maxwell's equations. It covers electrostatics, magnetostatics, electrodynamics, and the propagation of electromagnetic waves in vacuum and matter.
4.11.1. ELM/Electrostatics: Electric Field and Gauss's Law (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top
Analysis of stationary charges, the vector nature of the electric field, and the application of Gauss's Law to symmetric engineering configurations.
Topics:
Core
- Coulomb's law for point charges and the principle of linear superposition
- The electric field vector \(\vec{E}\) for discrete and continuous charge distributions
- Gauss's Law in integral form and its relation to enclosed charge
- Differential form of Gauss's Law: \(\nabla \cdot \vec{E} = \rho/\epsilon_0\)
- Applications of Gauss's Law to spherical and cylindrical symmetry
- The Divergence Theorem applied to electrostatic fields
Learning Outcomes:
Core:
- Calculate the electrostatic force on a charge distribution using superposition [Usage]
- Apply Gauss's Law to find the electric field for systems with high symmetry [Usage]
- Evaluate the electric flux through surfaces of engineering interest [Assessment]
- Determine volume charge density from a given expression of the electric field [Usage]
4.11.2. ELM/Electric Potential and Poisson/Laplace Equations (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top
The scalar potential formulation of electrostatics and the solution of boundary value problems relevant to capacitor and electrode design.
Topics:
Core
- Definition of the scalar potential \(V\) and \(\vec{E} = -\nabla V\)
- Calculating potential for continuous charge distributions
- Poisson's equation \(\nabla^2 V = -\rho/\epsilon_0\) and Laplace's equation
- Solution of Laplace's equation via separation of variables for engineering geometries
- The method of images for computing fields near conducting boundaries
Learning Outcomes:
Core:
- Compute the electrostatic potential energy of a charge configuration [Usage]
- Derive the electric field vector from a given scalar potential [Usage]
- Solve Laplace's equation for a practical engineering geometry with specified boundary conditions [Assessment]
- Apply the method of images to engineering problems involving grounded conductors [Usage]
4.11.3. ELM/Electrostatic Energy and Dielectrics (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top
Energy storage in electric fields, capacitor design, and the macroscopic behavior of dielectric materials used in electrical engineering.
Topics:
Core
- Energy density in the electric field: \(u = \frac{1}{2}\epsilon_0 E^2\)
- Capacitance \(C = Q/V\) for standard engineering geometries
- The displacement vector \(\vec{D}\) and Gauss's Law in dielectric materials
- Linear dielectrics, susceptibility, and relative permittivity \(\epsilon_r\)
- Boundary conditions for \(\vec{E}\) and \(\vec{D}\) at material interfaces
Learning Outcomes:
Core:
- Calculate the capacitance of parallel-plate and coaxial capacitors filled with dielectrics [Usage]
- Evaluate bound charge distributions in polarized dielectric materials [Assessment]
- Solve for electric fields on both sides of a dielectric interface using boundary conditions [Usage]
- Analyze the force on a dielectric slab in a partially inserted capacitor [Assessment]
4.11.4. ELM/Magnetostatics: Biot-Savart and Ampere's Laws (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top
The physics of steady currents, magnetic field generation, and forces on moving charges, forming the basis of motor and transformer design.
Topics:
Core
- Lorentz force law: \(\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})\)
- Magnetic force on current-carrying wires and loops
- Biot-Savart Law for the magnetic field of a current element
- Ampere's Law in integral form for high-symmetry engineering configurations
- The magnetic vector potential \(\vec{A}\) and \(\vec{B} = \nabla \times \vec{A}\)
Learning Outcomes:
Core:
- Calculate the magnetic field of solenoids and toroids using Ampere's Law [Usage]
- Compute the magnetic field on the axis of a current loop using the Biot-Savart Law [Usage]
- Verify that a given magnetic field satisfies \(\nabla \cdot \vec{B} = 0\) [Assessment]
- Analyze the torque on a current loop in a non-uniform magnetic field [Assessment]
4.11.5. ELM/Magnetic Properties of Matter (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top
Magnetization of materials, bound currents, and the classification of magnetic media relevant to transformer core and permanent magnet design.
Topics:
Core
- The magnetization vector \(\vec{M}\) as magnetic dipole moment per unit volume
- The magnetic field intensity \(\vec{H}\) and Ampere's Law in matter
- Physical principles of diamagnetism, paramagnetism, and ferromagnetism
- Ferromagnetic domains and the hysteresis loop for engineering material selection
- Linear magnetic media and magnetic permeability \(\mu\)
Learning Outcomes:
Core:
- Find bound current distributions for magnetized engineering materials [Usage]
- Classify materials as diamagnetic, paramagnetic, or ferromagnetic for engineering application suitability [Assessment]
- Analyze energy loss per cycle from a ferromagnetic hysteresis loop for transformer core selection [Assessment]
4.11.6. ELM/Electrodynamics: Faraday's Law and Induction (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top
Time-dependent magnetic fields and electromagnetic induction, foundational to generators, transformers, and electric motors.
Topics:
Core
- Faraday's Law of induction and Lenz's Law
- Self-inductance \(L\) and the back-EMF in engineering inductors
- Mutual inductance \(M\) and transformer principles
- Energy stored in the magnetic field of inductors
- Eddy currents, magnetic braking, and core loss in electrical machines
Learning Outcomes:
Core:
- Calculate the induced EMF in a rotating coil and relate it to generator operation [Usage]
- Apply Lenz's Law to determine the direction of induced currents in engineering scenarios [Assessment]
- Compute the magnetic energy stored in a solenoid or toroidal inductor [Usage]
- Evaluate mutual inductance between coupled coils for transformer design [Assessment]
4.11.7. ELM/Electric Current, Circuits, and Kirchhoff's Laws (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top
Study of electric charge flow, resistance, and DC circuit analysis using Kirchhoff's laws, foundational to all electrical engineering.
Topics:
Core
- Definition of current, current density, and the continuity equation
- Ohm's law, resistivity, and temperature dependence of resistance
- Kirchhoff's Current Law (KCL) for circuit node analysis
- Kirchhoff's Voltage Law (KVL) for circuit loop analysis
- Series and parallel circuit simplification and equivalent resistance
- RC and RL circuit transients and engineering time constants
Learning Outcomes:
Core:
- Apply KCL and KVL to solve multi-loop DC engineering circuits [Usage]
- Calculate power dissipated in resistive circuit elements [Assessment]
- Analyze the transient response of RC and RL circuits and determine the time constant [Usage]
- Design a resistor network to meet specified voltage division or current distribution requirements [Assessment]
4.11.8. ELM/Maxwell's Equations and Gauge Transformations ↑ Back to top
The unified set of equations governing all classical electromagnetic phenomena and the energy/momentum carried by electromagnetic fields.
Topics:
Core
- Maxwell's displacement current and its role in completing Ampere's Law
- The complete set of four Maxwell's equations in integral and differential forms
- Poynting's theorem and energy conservation in electromagnetic fields
- The Poynting vector \(\vec{S} = \vec{E} \times \vec{H}\) as energy flux density
- Gauge invariance and the formulation of potentials in engineering electrodynamics
Learning Outcomes:
Core:
- Calculate the displacement current in engineering capacitor circuits [Usage]
- State all four Maxwell equations and identify their physical content [Familiarity]
- Analyze the energy flow and power dissipation in engineering resistive and reactive components [Assessment]
- Compute the radiation pressure exerted by an electromagnetic wave on a reflective engineering surface [Usage]
4.11.9. ELM/Electromagnetic Waves and Propagation in Media ↑ Back to top
The propagation of electromagnetic waves in vacuum, dielectrics, and conductors, fundamental to antenna design, wireless communications, and photonics.
Topics:
Core
- Derivation of the electromagnetic wave equation from Maxwell's equations
- Monochromatic plane wave solutions and their polarization states
- Energy density, intensity, and momentum of plane waves
- Wave propagation in conducting media and the skin depth \(\delta\) for shielding design
- Reflection and refraction at interfaces for optical and RF engineering
Learning Outcomes:
Core:
- Derive the dispersion relation and relate the wave speed to medium properties [Usage]
- Determine the polarization state of a wave from its field vector components [Assessment]
- Analyze how skin depth varies with frequency and select shielding materials accordingly [Assessment]
- Apply Fresnel equations to calculate transmission and reflection at material interfaces [Usage]