LL8 Section 21 j mean charge flux density current density chargeareatime Constant current The flow in and out of every volume element is constant By continuity No charge builds up or is depleted at any point ID: 674412
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Slide1
Current density and conductivity
LL8 Section 21Slide2
j
= mean charge flux density
= current density
= charge/area-timeSlide3
Constant current:
The flow in and out of every volume element is constant.
By continuity
No charge builds up or is depleted at any point. Slide4
To maintain constant current,
E
must be constant.
That means there is no displacement current.
The
H-field from constant
j is constant.
A potential fieldSlide5
These 4 equations are insufficient to solve for the 6
unknowns
j
and
E
.
For a homogeneous isotropic conductor, Ohm’s law usually holds.
s
= “electrical conductivity”
In a homogeneous conductor,
s
is spatially uniform.Slide6
Laplace’s equation holds in a homogenous linear conductor when current is constant
For constant current,
is not spatially uniform,
and
E
is not zero inside the conductorSlide7
Boundary conditions for
j
and
E
Normal components of current density must be equal at the boundary due to charge conservation.
All charges incident from the left must cross to the right.Slide8
The tangential electric field component is continuousSlide9
Boundary conditions at the boundary between a conductor and a dielectric
No charge crosses into the insulator
On both sides , assuming no extraneous charge on the interface.Slide10
Electric field does work on the charge
de
Power
=
Power per unit volume
Dissipated as heat since current stays constant
For a homogeneous conductor Slide11
Evolution of heat causes increase in entropy.
Since the total entropy of the body must
increase
.
For homogeneous linear conductorsSlide12
For anisotropic bodies such as crystals,
j
need not be parallel to
E
.
Conductivity tensor
Positive, since
Symmetric
Onsager’s principle
From volume
5
Statistical
Physics section 120, “Symmetry of kinetic coefficients.”
A cubic crystal behaves as an isotropic body, since all three principal values of
sik are the same.