## PHYS2300 Physics 3- Fields and Energy

### 25 creditsClass Size: 250

Module manager: Dr Michael Ries
Email: M.E.Ries@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2023/24

### This module is mutually exclusive with

 PHYS2340 Electromagnetism (Geophysics) PHYS2350 Electromagnetism (Joint Honours)

This module is not approved as a discovery module

### Objectives

By the end of the module you should be able to:

Electromagentism

- use the integral versions of Maxwell's equations to explain the concepts of electric fields and potentials, magnetic fields and magnetic induction, and to calculate these fields in cases of simple symmetric geometry;
- calculate the force on a moving charge in an electric and magnetic field and the force on a current carrying conductor, and to calculate the energy stored in electric and magnetic fields;
- analyse simple AC circuits containing resistors, capacitors and inductors;
- state Maxwell's equations in both integral and differential form and discuss their derivation from the physical laws of electromagnetism, in vacuo and in dielectric and magnetic media;

Thermodynamics and Statistical Physics

- give examples of the emergence of thermodynamic phenomena in systems with large numbers of particles;
- use the Boltzmann factor to calculate occupation probabilities of states;
- use Boltzmann, Fermi-Dirac or Bose-Einstein statistics as appropriate to discuss basic thermodynamic properties of the two level paramagnet, the degenerate electron gas and blackbody radiation;
- discuss the concept of entropy from both the thermodynamic and statistical points of view and calculate entropy changes in irreversible processes;
- define enthalpy, the Helmholtz function and the Gibbs function and discuss their utility;
- state and discuss the four laws of thermodynamics, including various alternative formulations of each law;
- use these laws, and Maxwell relations to solve simple thermodynamic problems;
- describe the phase diagram for a one-component system, derive the Clausius-Clapeyron equation and use it to solve problems relating to the dependence of a phase transition on temperature and pressure.

Learning outcomes
Students will be able to demonstrate knowledge, understanding and application of the following:

In electromagnetism:
1. Electric and Magnetic fields, Biot-Savart law for a point charge and Lorentz force;
2. Maxwell’s Equations both “microscopic” and “macroscopic”;
3. Electric and Magnetic potential, Poisson’s equation;
4. Wave equation, EM waves, EM Spectrum and the Poynting vector;
5. AC circuits (LCR), complex impedance, transients, resonance.

In thermal physics and statistical mechanics:
1. First, second and third laws of Thermodynamics;
2. Maxwell relations, phase equilibrium and the Clausius-Clapeyron equation;
3. Macrostates and Microstates;
4. Boltzmann statistics for distinguishable particles;
5. Statistics of distinguishable and indistinguishable particles: Partition functions. Two-level paramagnet. Introduction to Fermi-Dirac and Bose-Einstein statistics.

Skills outcomes
Understanding of core electromagneetism and thermodynamics

### Syllabus

ELECTROMAGNETISM

Electric and Magnetic Fields: E field, Gauss; B field, Ampere; Magnetic induction, Faraday, Lenz.
AC currents: in resistors inductors and capacitors, LCR circuits, Complex impedance, Resonance.
Maxwell's Equations: (A) In vacuo with charges - Poisson; Magnetostatics, Displacement current, Maxwell's extension of Ampere's law; EM waves in vacuo,Energy and momentum in EM waves, EM spectrum. (B) In dielectric and magnetic media - Polarization and local fields; Magnetization; Summary of Maxwell's equations;

THERMODYNAMICS & STATISTICAL PHYSICS

Thermal Physics

Revision: First law; isothermal, adiabatic and quasi-static reversible changes; equations of state.

Second law, and entropy as a measure of disorder. Calculation of entropy change in irreversible processes.
Thermodynamic potentials: enthalpy, Helmholtz and Gibbs free energies. Maxwell relations, phase equilibrium and the Clausius-Clapeyron equation.
Third law.

Statistical Physics

Macrostates and Microstates.
Boltzmann statistics for distinguishable particles. Partition functions. Two-level paramagnet.
Statistics of indistinguishable particles. Introduction to Fermi-Dirac and Bose-Einstein statistics.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 11 2.00 22.00 Lecture 44 1.00 44.00 Private study hours 184.00 Total Contact hours 66.00 Total hours (100hr per 10 credits) 250.00

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Regular coursework 20.00 Total percentage (Assessment Coursework) 20.00

Resit will be in standard exam format.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 3 hr 00 mins 80.00 Total percentage (Assessment Exams) 80.00

Students will have to complete an in-person exam at the end of the module. This will take place during the examinations period at the end of the semester and will be time bound.