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THE UNIVERSITY OF TEXAS AT EL PASO
EE3321 Electromagnetic Field Theory
Lesson 5
1.
Gauss’ Law
Coulomb's law is actually a special case of Gauss's Law, a more fundamental description of the
relationship between the distribution of electric charge in space and the resulting electric field.
Gauss's law is one of Maxwell's equations, a set of four laws governing electromagnetics.
The
law bears the name of Karl Friedrich Gauss (17551855), one of the greatest mathematicians of
all time who also made significant contributions to theoretical physics.
In differential form, Gauss' law states that the divergence of the E field is proportional to the
charge density that produces it:
where
•
ρ is the total electric charge density (in units of C/m³).
•
is the electric constant, a fundamental constant of nature
Exercise:
Suppose that a charge is distributed in a sphere of radius R =1.
In the region 0 < R <
1, the electric field is given by E = 5 x 10
– 6
/R
R.
Find the charge density in this region.
Another interpretation of the law states “that the total electric flux
Ψ
through a closed surface
must be equal to the total enclosed charge.”
In integral form we write
∫ d
Ψ
= Q
Exercise:
What is the total flux out of a spherical surface around a point charge?
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View Full DocumentTHE UNIVERSITY OF TEXAS AT EL PASO
Exercise: Consider the case of an electric dipole.
What is the total flux coming out of the
rectangular surface?
2.
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 Fall '08
 FLORES
 Electromagnet

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