Lesson_5_-_Potential

# Lesson_5_-_Potential - THE UNIVERSITY OF TEXAS AT EL PASO...

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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 (1755-1855), 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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THE 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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Lesson_5_-_Potential - THE UNIVERSITY OF TEXAS AT EL PASO...

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