Capacitive and Inductive Circuits and Components

Acquire an understanding of the concepts of electrostatics (electric force, electric field, electric potential); magnetostatics (magnetic force, magnetic field); and induction (induced electric force, inductance); and apply them to electrical engineering applications.

- Calculate the effect of electric forces on electric charges

- Calculate the electric field created by charge distributions.

- Apply Gauss's theorem using simple examples.

- Calculate the potential energy and the electrostatic potential.

- Understand the concept of capacitance and calculate the capacitance of capacitors

- Calculate the electrical energy of simple systems

- Calculate the effect of magnetic forces on a charged particle.

- Calculate the magnetic field created by current density distributions.

- Apply Ampère's theorem using simple examples.

- Understand magnetic induction and calculate inductance

- Calculate the magnetic energy of simple systems

Required prerequisites:

Knowledge of vector calculus, cylindrical and spherical coordinate systems, differential operators, and basic trigonometric functions.

Recommended prerequisites:

Knowledge of the fundamental principles of mechanics (conservation of energy, fundamental principle of dynamics).

Capacitive Circuits

I. The Concept of Electric Charge – Coulomb’s Law – Electric Force.

II. Electric Field – Field Lines – Electrostatic Dipole in an External Field.

III. Electric Potential – Equipotential Surface – Electrostatic Influence and Equilibrium of Conductors. Determining E from the Potential.

IV. Electric Flux – Gauss's Theorem.

V. Capacitor: dielectric – capacitance – energy – capacitor bank. Electrical energy

 Inductive Circuits

I. Magnetic Forces – Effects of a magnetic field on a charge and on a current; the Hall effect.

II. Magnetic Field Created by Steady Currents: Biot–Savart Law, Calculation of the Magnetic Field Around Simple Objects (wire, coil).

III. Ampère's Theorem, Calculation of the Electric Field Around a Wire, Coil, and Solenoid. Applications to Helmholtz Coils and Coaxial Cables.

IV. Electromagnetic Induction: Magnetic flux, Faraday's law, Lenz's law, inductance, mutual inductance, and self-induction. Magnetic energy.