Cristina Lazzeroni c.lazzeroni@bham.acepweb2.ph.bham.ac.uk/user/lazzeroni/EM2_2017/Lecture1_EM2.pdf · Electromagnetism by Grant and Phillips Basic Electromagnetism by E R Dobb Electromagnetic

Electromagnetism II

Cristina Lazzeronic.lazzeroni@bham.ac.uk

0300953 0320266 Physics Maths

Electromagnetism: branch of physics studying electromagnetic force

Electromagnetic force is all pervasive, infinite range

Hydrogen atom:EM force is ~1040 gravitational force of proton on electron On small scales, EM dominates

EM is the force that binds atoms together in molecules and solids

EM has impact on large scale too

In a geomagnetic storm, a surge in the flux of charged particles temporarily altersEarth's magnetic field, which induces electric fields in Earth's atmosphere, thuscausing surges in electrical power grids. (Artist's impression; sizes are not to scale)

Light, X-rays, radar, TV signals, microwaves are allforms of radiation

Magnetic core memory (1954) is an application of Ampère's law. Each core stores one bit of data.

Energy is most conveniently carried in EM form

Communication carried by EM waves

Many of the concepts of EM reappear in other areas ofmodern physics

Plus electrical signals cause the heart to beat,and allow our brain to think and seeAnd much more

A good understanding of EM is essential for any scientist

And for developing future technologies

James Clerk Maxwell

Born in 1831 in EdinburghDied in 1879 in Cambridge

Treatise on Electricityand Magnetism20 equations in 20 variables

He made one vital contribution:realized that EM laws wereincomplete.This missing part unlocked themystery of light.

Oliver Heaviside (1850-1925)

Reformulated Maxwell’s original20 eqs into four via vector calculus notation

Now universally known asMaxwell’s equations

This subject is made easier by the fact that all boils down to a set of equations:

Maxwell (core) + Lorentz (force on a charge in em field) equations

Maxwell’s 4 equations describe the whole of electricity and magnetism and unify the electric and magnetic forces into one theory of electromagnetism.They also show that electromagnetic waves are Lorentzinvariant.

Recommended books:

Electromagnetism by Grant and PhillipsBasic Electromagnetism by E R Dobb Electromagnetic Fields and Waves by D Corson and P LorrainElectricity and Magnetism by Bleaney and BleaneyElectricity and Magnetism by Cottingham and Greenwood

Aims of Lecture 1 and 2:

Review and extend concepts of Electromagnetism I

Write Maxwell’s equations in free spaceusing vector calculus introduced last Term

Lecture 1:

Write Maxwell’s equations in integral form (using volume,surface and line integrals) in free space (no dielectrics or magnetic materials and no displacement current) derived from:

Gauss’ Law for Electric FieldsGauss’ Law for Magnetic FieldsFaradays’ LawAmpere’s Law

Gauss’ LawProvides a direct way to computethe electric flux.In presence of symmetry, allowsto easily compute electric field.

No magnetic monopoles

Example:

The charge density ρ in a certain region has the form:

Where b is a constant.Derive expressions for the electric field produced by thischarge density.

Faraday’s LawDescribes electric potential induced by varying magnetic field

Lenz’s Law: the direction of an induced current (if one wereto flow) is such that its effect would oppose the change in magnetic flux which gave rise to the current

Ampere’s Law

The integral of B around any closed mathematical path equalsµ0 times the current intercepted by the area spanning the path

Example:

Calculate the magnetic field B inside a long solidcylindrical conductor carrying uniformly distributedcurrent I

Lorentz’s Force

If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force

Summary: Maxwell’s equations

Digression: vector calculus

See also Maths notes from lectures 22,23,24,25 of Term 1

Next Lecture:

Introduce the differential form of Maxwell’s equations

Discuss what is missing from the laws of electromagnetism

Recommended readings:Grant+Phillips: 1.4, 1.4.1, 1.4.2, 4.4, 4.4.1, 6.1, 6.1.1, 6.1.2

Example:

The charge density ρ in a certain region has the form:

Where b is a constant.Derive expressions for the electric field produced by thischarge density.

Example:

The charge density ρ in a certain region has the form:

Where b is a constant.Derive expressions for the electric field produced by thischarge density.

Example:

Calculate the magnetic field B inside a long solidcylindrical conductor carrying uniformly distributedcurrent I

Example:

Calculate the magnetic field B inside a long solidcylindrical conductor carrying uniformly distributedcurrent I