ENE 325 Electromagnetic Fields and Waves. Lecture 3 Gauss’s law and applications, Divergence, and Point Form of Gauss’s law. Review (1). Coulomb’s law Coulomb’s forc e electric field intensity or V/m.
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ENE 325Electromagnetic Fields and Waves
Lecture 3 Gauss’s law and applications, Divergence, and Point Form of Gauss’s law
2. Select a Gaussian surface
3.Drat a fixed distance is constant and normal to a Gaussian surface, can be pulled out from the integral.
1. From symmetry,
2. Select a Gaussian surface with radius and length h.
3. D at a fixed distance is constant and normal to a Gaussian surface, can be pulled out from the integral. ant and normal to a Gaussian surface, can be pulled out from the integral.
Ex3 A parallel plate capacitor has surface charge +S located underneath a top plate and surface charge -S located on a bottom plate. Use Gauss’s law to find and between plates.
Ex5 A point charge of 0.25 C is located at r = 0 and uniform surface charge densities are located as follows: 2 mC/m2 at r = 1 cm and -0.6 mC/m2 at r = 1.8 cm. Calculate at
c) r = 2.5 cm
where = volume differential element
or we can write in derivative form as
It is apparent that
therefore we can write a differential or a point form of Gauss’s law as
For a cylindrical coordinate:
For a spherical coordinate:
The plunger moves up and
down indicating net movement
of molecules out and in,
An integral form of Gauss’s law can also be written as
Ex7Let C/m2 for a radius r = 0 to r = 3 m in a cylindrical coordinate system and for r > 3 m. Determine a charge density at each location.
Ex8 Let in a cylindrical coordinate system. Determine both terms of the divergence theorem for a volume enclosed by r = 1 m, r = 2 m, z = 0 m, and z = 10 m.