Capacitive and inductive circuits and components

Acquire the concepts of electrostatics: electric force, electric field, electric potential; magnetostatics: magnetic force, magnetic field; induction: induced electric force, inductance and implement them for applications in electrical engineering.

- Calculate the action of electrical forces on electrical charges

- Calculate the electric field created by charge distributions.

- Apply Gauss' theorem to simple examples.

- Calculate the potential energy and the electrostatic potential.

- Understand the concept of capacitance and calculate capacitances of capacitors

- Calculate the electrical energy of simple systems

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

- Calculate the magnetic field created by current density distributions.

- Apply Ampere's theorem to simple examples.

- Understand magnetic induction and calculate inductances

- Calculate the magnetic energy of simple systems

Required Prerequisites:

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

Recommended prerequisites:

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

Capacitive Circuits

I- Concept of electric charge - Coulomb's law - Electric force.

II- Electric field - Field lines - Electrostatic dipole in an external field.

III- Electrical potential - Equipotential - Electrostatic influence and equilibrium of conductors. Determination of E from the potential.

IV- Electrical flow - Gauss's theorem.

V- Capacitor : dielectric - capacity - energy - capacitor grouping. Electrical energy

 Inductive Circuits

I- Magnetic forces - Effects of the magnetic field on a charge, on a current, Hall effect.

II- Magnetic field created by permanent currents: Biot and Savart's law, calculation of field of simple object (wire, coil).

III- Ampere's theorem, calculation of field of a wire, coil, solenoid. Applications to Helmoltz coils, coaxial cable.

IV- Electromagnetic induction phenomenon: Magnetic field flow, Faraday's law, Lenz's law, inductance, mutual inductance and self-induction. Magnetic energy.