## Flux

Flux IE. Water in an irrigation ditch of width w = 3.22 m and depth d = 1.04 m flows with a speed of 0.20i m/s. The mass flux of the flowing water through an imaginary surface is the product of the

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# Gauss Law

## QUESTIONS Gauss Law

## Applying Gauss’ Law: Spherical Symmetry

## Sample Problem Gauss Law

## Two Conducting Plates

## Applying Gauss’ Law: Planar Symmetry

## Sample Problem Gauss Law

## Applying Gauss’ Law: Cylindrical Symmetry

## Sample Problem GAUSS Law

## The Conductor Removed

QUESTIONS Gauss Law A sudace has the area vector A = (2l + 31) m2 What is the flux of an electric field through it if the field is (a) E = 4i N/C and (b) E = 4k N/C What is J dA for (a) a square of edge length a (b) a circle of radius r and …

Applying Gauss’ Law: Spherical Symmetry Here we use Gauss’ law to prove the two shell theorems presented without proof in A shell of uniform charge attracts or repels a charged particle: that is outside the shell as if all the shell’s charge were concentrated at the center of the shell A shell of uniform charge exerts …

Sample Problem Gauss Law shows portions of two large parallel nonconducting b sheets each with a fixed uniform charge on one side The magnitudes of the surface charge densities are for the positively charged sheet and a for the negatively charged sheet Find the electric field E (a) to the left of the sheets (b) between the sheets and (c) to …

Two Conducting Plates a cross section of a thin infinite conducting plate with excess positive charge we know that this excess charge lies on the surface of the plate Since the plate is thin and very large we can assume that essentially all the excess charge is on the two large faces of the plate If there is no …

Applying Gauss’ Law: Planar Symmetry Nonconducting Sheet a portion of a thin, infinite, nonconducting sheet with a uniform (positive) surface charge density T A sheet of thin plastic wrap union charged on one side can serve as a simple model Let us find the electric field E a distancer in front of the sheet-A useful Gaussian surface …

Sample Problem Gauss Law The visible portion of a lightning strike is preceded by an invisible stage in which a column of electrons extends downward from a cloud to the ground These electrons come from the cloud and from air molecules that are ionized within the column. The linear charge density A along the column is typically -I X …

Applying Gauss’ Law: Cylindrical Symmetry section of an infinitely long cylindrical plastic rod with a uniform positive linear charge density A. Let us find an expression for the magnitude of the electric field E at a distance r from the axis of the rod Our Gaussian surface should match the symmetry of the problem which is cylindrical. We choose …

Sample Problem GAUSS Law a cross section of a spherical metal shell of inner radius R. A point charge of -5.0 IlC is located at a distance R/2 from the center of the shell If the shell is electrically neutral what are the (induced) charges on its inner and outer surfaces’ Are those charges distribution distributed What is the …

The Conductor Removed Suppose that by some magic the excess charges could be “frozen” into position on the conductor’s surface perhaps by embedding them in a thin ‘plastic coating and suppose that then the conductor could be removed completely This is equivalent to enlarging the cavity of until it consumes the entire conductor leaving only the charges The electric …