Lecture 6

# Lecture 6 - PEP112 Spring 2008 Prof Svetlana Malinovskaya 4...

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PEP112 – Spring 2008 Prof. Svetlana Malinovskaya 4 February 2008 Gauss’s Law

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Introduction • We calculated electric field of various shapes by starting from Coulomb’s law for the electric field of a point charge. • Now we’ll learn how some important electric fields can be deduced from the shape of the charge distribution. • Gauss’s Law and Coulomb’s Law are equivalent and can be derived from each other, but Gauss’s Law gives different perspective. It may be applied not only to electrostatics but also to electrodynamics.
Symmetry • Symmetry is an especially important idea in physics and mathematics. • We say that a charge distribution is symmetric if there is a group of geometrical transformations that don’t cause any physical change. Such transformations are translation, rotation, and reflection. • If after transformation you cannot reveal any change in charge distribution, then we say that charge distribution is symmetric under that particular transformation.

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Example: Cylindrical Symmetry • The symmetry of the electric field must match the symmetry of the charge distribution.
The Electric Field of a Cylinder • The electric field is radial, pointing out from the cylinder. This is the only one electric field shape that matches the symmetry of the charge distribution.

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Lecture 6 - PEP112 Spring 2008 Prof Svetlana Malinovskaya 4...

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