Notes on Chapter 23

Notes on Chapter 23 - Chapter 23 Gausss Law 23-1 What is...

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10 June 2010 1 Chapter 23 – Gauss’s Law Gauss’s Law relates the electric fields at points on a (closed) surface to the net charge enclosed by that surface Gauss’s Law is particularly useful (and powerful) when it uses the symmetry of the charge distribution. The example here we use spherical symmetry 23-1 What is Physics?

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10 June 2010 2 A ˆ A An = ˆ () AAn −= Area vector Flux The volume flow rate is: ( cos ) (1) vA θ Φ= This is an example of flux Volume flux in this case 23-2
10 June 2010 3 If Φ = 0 then whatever flows into the surface must flow out If Φ > 0 the more flow out than flow in If Φ < 0 then more flow in than flows out (1) Can be written as a scalar (or dot) product : cos vA v A θ Φ= =

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10 June 2010 4 Even though flux means “ to flow ”, it is not always that a quantity has to flow in order to define flux. In particular the electric field does not flow but we can still define the electric flux, Φ E Electric flux There are two types of surfaces, open surface and closed surface Open (flat) surface Open (curved) surface Examples of closed surfaces 23-3 Gauss’s Law deals only with closed surfaces
10 June 2010 5 In order to calculate the electric field or the net charge of a particular problem we often use an imaginary closed surface, called the Gaussian surface . The shape is often determined by the symmetry of the problem We define the electric flux for the Gaussian surface shown as E EA Φ = SI unit of electric flux is newton . square-meter per coulomb

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Notes on Chapter 23 - Chapter 23 Gausss Law 23-1 What is...

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