23-06-2012, 02:21 PM
Electrostatics and Magnetostatics
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In the static regime, electromagnetic quantities do not vary as a
function of time. We have two main cases:
ELECTROSTATICS – The electric charges do not change
postion in time. Therefore, ρ, E and D are constant and there is no
magnetic field H, since there is no current density J.
MAGNETOSTATICS – The charge crossing a given crosssection
(current) does not vary in time. Therefore, J, H and B are
constant. Although charges are moving, the steady current
maintains a constant charge density ρ in space and the electric
field E is static.
Most electrostatic problems can be solved by direct application of
Poisson equation or of Gauss law.
Analytical solutions are usually possible only for simplified
geometries and charge distributions, and numerical solutions are
necessary for most general problems.
The potential φ indicates then the work necessary to move an
infinitesimal positive probe charge from distance r (point b) to
infinity (point a) for negative Q, or conversely to move the probe
from infinity to distance r for positive Q (remember that the work is
done against the field). The probe charge should be infinitesimal,
not to perturb the potential established by the charge Q.
The work per unit charge done by the fields to move a probe charge
between two points, is usually called Electromotive Force ( emf ).
Dimensionally, the emf really represents work rather than an actual
force.