Lecture 7

Lecture 7 - PEP112 Spring 2008 Prof. Svetlana Malinovskaya...

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PEP112 – Spring 2008 Prof. Svetlana Malinovskaya 6 February 2008 Gauss’s Law. Applications
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Curved Surface and Closed Surface • The electric flux through a curved or closed surface is the sum of the fluxes through smaller pieces of the surface, giving e surface e surface E dA E dA Φ= > G G G G If the electric field is everywhere tangent to the surface, the electric flux through the surface is zero. If the electric field is everywhere perpendicular to the surface and is uniform, then flux is . EA Φ =
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Gauss’s Law Let’s calculate flux for a point charge. We imagine Gaussian surface around the point charge. This Gaussian surface has same symmetry as the electric field. The electric field is perpendicular to the surface at every point on the surface and has same magnitude. The flux is the surface integral: 22 0 2 2 00 /(4 ) 4 4 4 e surface es p h e r e Ed A Eq r A r EA qq r r π επ πε ε Φ= == = = > G G G
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We found the flux for the positive charge. It applies to a negative charge as well. The flux is negative being the dot product of pointing out area vector and pointing inward the electric field. The flux does not depend on the radius of the Gaussian sphere. The net electric flux is zero through a closed surface that does not contain any net charge. Charges outside the surface do not produce a net flux through the surface.
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This note was uploaded on 04/09/2008 for the course PEP 112 taught by Professor Whittaker during the Spring '07 term at Stevens.

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Lecture 7 - PEP112 Spring 2008 Prof. Svetlana Malinovskaya...

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