# PX120 Electricity & Magnetism

## Lecturer: Erwin Verwichte

## Weighting: 12 CATS

This module is largely concerned with the great developments in electricity and magnetism, which took place during the nineteenth century. The origins and properties of electric and magnetic fields in free space and in materials are tested in some detail and all the basic levels up to, but not including, Maxwell's equations are considered. In addition the module deals with both dc and ac circuit theory including the use of complex impedance.

**Aims:**

To introduce the properties of electrostatic and magnetic fields, and their interaction with dielectrics, conductors and magnetic materials. To introduce some of their practical effects and the behaviour of simple passive circuits and networks.

**Objectives:**

At the end of this module you should:

- Understand the concepts of charge, field and flux.
- Be able to compute the electrostatic and magnetic fields for simple distributions of monopoles or dipoles.
- Understand in outline the interaction between electrostatic or magnetic fields and different classes of material (dielectric materials, dia-, para-, and ferro- magnetic materials).
- Understand the phenomena of capacitance and inductance.
- Know the laws of electromagnetic induction and be able to apply them to calculate self- and mutual inductance. You should understand the behaviour of electricity generators and electric motors, and be able to find the energy in simple magnetic fields.
- Understand the phenomenon of resistance and be able to calculate the current and potential distributions in simple DC networks
- Know how the various passive circuit elements (resistors, capacitors and inductors) behave when subject to alternating emf's and be able to use complex impedances to simplify such problems.
- Be able to explain the properties of simple LCR circuits.

**Syllabus:**

Introduction: Field forces, history, the concepts of charge and flux, stationary and moving charges.

Essential Mathematics I: Solid angle, integration and vectors, area as a vector, coordinate systems.

Elements: Gauss' Theorem, monopole and dipole sources.

Electrostatics:, electric field of a point charge, principle of superposition, application of Gauss' Theorem to **E**, Coulomb's law, work and electrical potential, exchange of electrostatic and kinetic energy.

The electric dipole: field and moment, addition of dipole moments, forces on dipoles in electric fields, dielectric materials and polarization.

Capacitance: capacitors, stored energy, capacitors in series, capacitors in parallel.

Magnetostatics: Magnetic field of a current, magnetic dipole and Gauss' Theorem, the Biot-Savart Law, Ampere's circuital law, forces on and between conductors, forces on individual moving charges, torque on a current loop/magnetic dipole, the dipole moment.

Electromagnetic Induction: Faraday's law, Lenz's principle, motional e.m.f., flux - cutting law, electric generators, electric motors, self-inductance, mutual inductance, magnetic energy, inductors in series and in parallel.

Magnetic dipoles in materials, magnetization, paramagnetics, diamagnets and ferromagnets, magnetization surface current.

D.C. Circuits: The electric circuit, energy relationships, Kirchoff's laws, Maxwell loop currents, use of symmetry, superposition principle, Thevenin's theorem, Norton's theorem.

Essential Mathematics II: Complex numbers, Euler's representation.

Transient Response: Capacitors, inductors, LCR circuits.

Sinusoidal Currents and EMF's: Capacitors, Inductors, Resistors, the concept of phasors, complex impedance, a.c. power and the power factor, series resonant LCR circuits, quality factor, voltage magnification, parallel resonant LCR circuit, filters, a.c. bridges.

**Commitment:** 30 Lectures + 10 problems classes

**Assessment:** 2 hour examination

This module has a home page.

**Recommended Text:** H D Young and R A Freedman, University Physics , Pearson. also W.J.Duffin, *Electricity and Magnetism*, McGraw-Hill; R Feynman, *Feynman Lectures on Physics vol. II*, Addison-Wesley.

**Leads from:** A level Physics

**Leads to:** PX 263 Electromagnetic Theory and Optics