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This text provides an outline of the applications of Gauss's Law in various scenarios, including the electric field of a sphere of charge, a spherical shell, a line of charge, and conductors and insulators.
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Hw: All Chapter 5 problems and exercises Electricity and Magnetism Physics 208 Dr. Tatiana Erukhimova Lectures 14-15
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Outline • Applications of Gauss’s Law - The single Fixed Charge • Field of a sphere of charge • Field of a spherical shell • A Line of Charge • Conductors and Insulators • The electric field of a conductor • The field in the cavity of a conductor; Faraday’s Cage
Solid conducting sphere with charge Q A E V r A r
Electric field of a ball of charge Q Electric field outside of a charged sphere is exactly the same as the electric field produced by a point charge, located at the center of the sphere, with charge equal to the total charge on the sphere.
Electric field of a spherical shell Q The field outside the shell is like that of a point charge, while the field everywhere inside the shell is zero.
A Charged, Thin Sheet of Insulating Material + + + + + + + + + + +
Conductors and insulators Charges reside at the surface of the conductor + + + + + + + + Conductor + + E=0 + + + + +
What have we learned about conductors? • There is no electric field inside a conductor • Net charge can only reside on the surface of a conductor • Any external electric field lines are perpendicular to the surface (there is no component of electric field that is tangent to the surface). • The electric potential within a conductor is constant
Two parallel conducting plates - + + + - + a - + + d (the total field at any point between the plates)
An Apparent Contradiction - + + + - + - + +
An Apparent Contradiction - + + + - + - + + Near the surface of any conductor in electrostatics
1) There is a conducting spherical shell, inner radius A and outer radius B. If you put a charge Q on it, find the charge density everywhere. 2) There is a conducting spherical shell, inner radius A and outer radius B. A charge Q is put at the center. If you put a charge Q2 on the shell, find the charge density everywhere.
A sphere of radius A has a charge Q uniformly spread throughout its volume. Find the difference in the electric potential, in other words, the voltage difference, between the center and a point 2A from the center.
There is a conducting spherical shell, inner radius A and outer radius B. A charge Q1 is put at the center. If you now put charge -2Q1 on the shell, find the charge density at r=A and r=B.
