Potentials and fields Flashcards
State the expressions for the electric and magnetic fields in terms of the gauge (scalar and
vector) potentials. Explain how the potentials
are used to eliminate one pair of Maxwell’s
equations.
Q34
Explain what is meant by a gauge transformation, gauge freedom and a gauge function
(gauge parameter).
The assignment of the gauge potentials to a physical field is not unique. A gauge transformation where φ(r, t) is an arbitrary scalar field, leaves the physical observables E and B invariant. This invariance creates a degree of freedom in choosing the gauge potentials
which is called the gauge freedom. Gauge freedom can be used to impose an arbitrary
functional condition, aka a gauge-fixing condition, on one of the four potentials or their
linear superposition.
Explain what is meant by a gauge-fixing condition. State the gauge fixing conditions for
(a) the Lorentz gauge (b) the Coulomb gauge.
Q36
. State the equations of motion for the gauge
(scalar and vector) potentials in the Lorentz
gauge. What are the advantages of this gauge?
Q37
State the expressions for the retarded scalar
and vector potentials in the Lorentz gauge.
Q38
. State the expressions for the Lienard-Wiechert
potentials also explaining the meaning of the
retarded position, time and velocity.
Q39
. State the expression for the electromagnetic
power irradiated by an electric dipole oscillating with frequency ω and amplitude p. Specify
the validity conditions for your expression.
Q40
Give an expression for the electromagnetic radiation reaction force. Discuss the problems
of this expression and explain how it should
be used in practice.
Q41
Explain the difference between the free charge
and the bound charge in regards to electromagnetic fields in dielectric media.
Q42
Explain what is meant by the polarisation P
of a dielectric medium.
Q43
Give expressions for the bound volume charge
and the bound surface charge of a polarised
dielectric medium.
Q44
Explain the difference between the macroscopic electric field and the microscopic electric
field in a polarised dielectric medium. Give the
expression for the divergence of of the macroscopic electric field inside a dielectric medium
in the presence of free charge %f and polarisation P.
Q45
State the expression for the electric displacement in a dielectric medium in terms of the
electric field and polarisation. Give the SI dimensions of the electric displacement.
Q46
State Gauss’s law for the electric displacement
D. Explain why the electric displacement field
of a point free charge does not necessarily obey
the Coulomb law.
Q47
Explain what is meant by the electric susceptibility, the permittivity and the dielectric constant of a linear dielectric material. State the
relationship between the electric field and the
electric displacement in a linear dielectric material.
See exam 2016 B(i) or written answers self test question 48
State the boundary conditions for the electric
field and the electric displacement at an interface between two dielectric media. Explain
how these follow from Maxwell’s equations.
(i) The orthogonal component of the D field is continuous across the interface. This follows from Gauss’s law combined with the absence of free charge at the interface.
(ii) The tangential component of the E field is continuous across the interface. This follows from Faraday’s law and the requirement that there is no divergence of the B-field at the interface.
Explain the difference between the free current and the bound current in a magnetised
medium.
Q50
Explain what is meant by the magnetisation
of a magnetised medium.
Q51
Give the expressions for the bound volume current and bound surface current in terms the
magnetisation of a medium.
Q52
. Give the expression for the curl of the macroscopic magnetic field inside a magnetised
medium in the presence of the free current Jf
and magnetisation M.
Q53
State the expression for the magnetic H field
in terms of the B field and the magnetisation.
Give the SI dimensions of the H field.
Q54
For a linear medium define what is meant by
the magnetic susceptibility and the magnetic
permeability. Explain the difference between
diamagnetic and paramagnetic materials.
Q55
. State the boundary conditions for the H field
and the B field at an interface between two
magnetised media. Explain how these follow
from Maxwell’s equations.
Q56
