ECE 106: Electricity and Magnetism

Sources and References

Equivalent UW courses — PHYS 122 (Waves, Electricity and Magnetism), PHYS 242 (Electricity and Magnetism 1), PHYS 124 (Modern Physics)

Primary textbook — Young, H. D. and Freedman, R. A. University Physics with Modern Physics, 15th ed., Pearson, 2019 (chapters 21-30 on electrostatics through electromagnetic induction).

Supplementary references — Griffiths, D. J. Introduction to Electrodynamics, 4th ed., Cambridge University Press, 2017; Hawkes, R., Iqbal, J., Mansour, F., Milner-Bolotin, M. and Williams, P. Physics for Scientists and Engineers: An Interactive Approach, 2nd ed., Nelson, 2018; Purcell, E. M. and Morin, D. J. Electricity and Magnetism, 3rd ed., Cambridge University Press, 2013.

Equivalent UW Courses

ECE 106 is the electromagnetism half of the two-term introductory physics sequence for electrical and computer engineers, and covers essentially the same static-field material as PHYS 122 in the physics major stream. Both courses move from Coulomb’s law through Gauss’s law, electric potential, capacitance, current, magnetic forces and fields, Ampere’s law, and Faraday induction. PHYS 242 is the second-year E&M course for physics majors and revisits this material at a more formal level using vector calculus and Poisson’s equation. PHYS 124 on modern physics covers relativity, photons, and early quantum mechanics and does not overlap with ECE 106 at all — it is grouped here only because it is the other half of first-year physics on the physics side.

What This Course Adds Beyond the Equivalents

Relative to PHYS 122, ECE 106 is tuned toward engineering applications: more time on capacitor and inductor geometries as circuit elements, on energy storage, and on simple motors, generators, and transformers. It spends less time on waves and optics (which ECE students pick up elsewhere) and treats dielectric and magnetic materials with an eye to engineering constitutive relations rather than atomic-scale derivations. Relative to PHYS 242, ECE 106 stays almost entirely in integral form and delays the full vector-calculus treatment of Maxwell’s equations to later ECE courses on electromagnetic fields and waves. The modern-physics content of PHYS 124 is entirely absent.

Topic Summary

Electric Charge, Coulomb’s Law, and Conductors

The course opens with discrete point charges, conductors versus insulators, and the inverse-square electrostatic force

\[ \vec{F}_{12} = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r^2} \hat{r}. \]

Superposition extends this to continuous distributions via integration over line, surface, and volume charge densities.

Electric Field and Field Lines

The field \( \vec{E} = \vec{F}/q \) is introduced as the force per unit test charge, with standard results for dipoles, rings, disks, and infinite lines computed by direct integration. Field lines give a qualitative picture of flux density and direction.

Electric Flux and Gauss’s Law

Gauss’s law

\[ \oint_S \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enc}}}{\varepsilon_0} \]

is the central symmetry tool: spherical, cylindrical, and planar symmetries let students recover field strengths without integration. Boundary conditions at conductor surfaces and the vanishing of interior fields in electrostatic equilibrium are emphasized.

Electric Potential and Potential Energy

Potential is defined by the path integral \( V(\vec{r}) = -\int_{\infty}^{\vec{r}} \vec{E} \cdot d\vec{\ell} \), with \( \vec{E} = -\nabla V \) as the local inverse. Equipotential surfaces, potential of charge distributions, and the energy stored in a charge configuration are computed for standard geometries.

Capacitance and Dielectrics

Capacitance \( C = Q/V \) is derived from first principles for parallel-plate, cylindrical, and spherical geometries. Dielectric insertion multiplies capacitance by the relative permittivity \( \kappa \), and the stored energy is \( U = \tfrac{1}{2} C V^2 \). Series and parallel combinations are treated as circuit elements.

Current, Resistance, and Ohm’s Law

Charge transport is described by current density \( \vec{J} = n q \vec{v}_d \) and Ohm’s law in microscopic form \( \vec{J} = \sigma \vec{E} \). Resistance, power dissipation \( P = I^2 R \), and temperature dependence of resistivity are covered briefly.

Magnetic Force and Magnetic Fields

The Lorentz force \( \vec{F} = q \vec{v} \times \vec{B} \) and force on current-carrying wires \( d\vec{F} = I\, d\vec{\ell} \times \vec{B} \) are introduced, followed by circular motion of charges, magnetic moments, and torques on current loops.

Biot-Savart and Ampere’s Law

Magnetic fields from currents are computed with the Biot-Savart law

\[ d\vec{B} = \frac{\mu_0}{4\pi} \frac{I\, d\vec{\ell} \times \hat{r}}{r^2} \]

and with Ampere’s law \( \oint \vec{B} \cdot d\vec{\ell} = \mu_0 I_{\text{enc}} \). The two approaches are contrasted: Ampere’s law for high-symmetry problems (long wires, solenoids, toroids), Biot-Savart for the general case.

Faraday’s Law and Induction

Faraday’s law \( \mathcal{E} = -d\Phi_B/dt \) and Lenz’s law fix the polarity of induced EMF. Motional EMF, eddy currents, the non-conservative nature of the induced electric field, and simple AC generators and DC motors are discussed qualitatively and quantitatively.

Self and Mutual Inductance

Self-inductance \( L \) is computed for solenoids and toroids, mutual inductance \( M \) for coupled coils, and magnetic energy storage \( U = \tfrac{1}{2} L I^2 \). Transformers and order-of-magnitude power-generation estimates close the course.