Basics Flashcards
Give definitions to the following structures in vector calculus • Scalar field • Vector field • Gradient of a scalar field • Divergence of a vector field • Curl of a vector field
Scalar field: a physical entity build out of scalars that obeys laws of evolution
Vector field: a physical entity build out of vectors that obeys laws of evolution
Gradient of a scalar field: the amount how much a field will change by moving in different direction “a derivative in all directions”
Divergence of a vector field: the amount how much a vector spreads out from the point in question
Curl of a vector field: the amount how much a vector swirls around the point in question
Give definitions to the following structures in vector calculus • Volume integral of a scalar field • Surface integral of a vector field • Line integral of a vector field
See question 2 self test questions
State Gauss’s theorem for the divergence of a
vector field.
See question 3 self test questions
State Stokes’s theorem for the curl of a vector
field.
See question 4 self test questions
State both the integral and the differential
form of the continuity equation for the electric charge.
See question 5 self test questions
State Maxwell’s four equations in differential
form.
See question 6 self test questions
State Maxwell’s four equations in integral
form.
See question 7 self test questions
State the expression for the displacement current density. Explain which physical law would
be violated by Maxwell’s equations if the latter were written without the displacement current.
See question 8 self test questions
State the expression for the force acting on a
point particle of charge Q moving with velocity
v in the presence of an electric field E and a
magnetic field B.
See question 9 self test questions
The last pair of Maxwell’s equations contain
time derivatives of the fields and can be viewed
as equations of motion (laws of evolution) for E
and B. The first pair of Maxwell’s equations do
not contain time derivatives and can be viewed
as constraints which the fields must obey at
any instant of time. Show that if at t = 0 the
fields satisfy the first pair of Maxwell’s equations (the constraints), then the time evolution
under the second pair of Maxwell’s equations
preserves the constraints automatically.
Not sure yet
Give the expression for the energy density of
an electromagnetic field. State the dimensions
of this quantity in SI units.
See question 11 self test questions
Give the expression for the energy density flow
(the Poynting vector). State the dimensions of
this quantity in SI units.
See question 12 self test questions
. State Poynting’s theorem for the work per
unit time done by an electromagnetic field on
charged matter inside a volume V.
See question 13 self test questions
Give the expression for the Cartesian components of Maxwell’s stress tensor.
See question 14 self test questions
State the expression, in terms of Maxwell’s
stress tensor for the net force exerted by the
electromagnetic field on charged matter inside
a volume V.
See question 15 self test questions
