Quizzes 3 A cube with 1.40 m edges is oriented as shown in the figure Suppose the cube sits in a uniform electric field of 10i ? What is the magnitude of the flux through the whole cube? What is the magnitude of the flux through the top side? How many sides have nonzero flux? q/eo D) q/6eo q/4eo 2 D) 1 4

Applying Gauss’s Law Can be used to determine total flux through a surface in simple cases Must have a great deal of symmetry to use easily charge q Charge in a long triangular channel What is flux out of one side?

Applying Gauss’s Law L R r Draw a cylinder with the desired radius inside the cylindrical charge Infinite cylinder radius R charge density  What is the electric field inside and outside the cylinder? Electric Field will point directly out from the axis No flux through end surfaces

Applying Gauss’s Law L R r Draw a cylinder with the desired radius outside the cylindrical charge R Infinite cylinder radius R charge density  What is the electric field inside and outside the cylinder? Electric Field will point directly out from the center No flux through endcaps

Applying Gauss’s Law Sphere volume: V = 4a3/3 R Sphere area: A = 4a2 Draw a Gaussian surface inside the sphere of radius r r R Sphere radius R charge density . What is E-field inside? What is the magnitude of the electric field inside the sphere at radius r? R3/30r2 r2/30R C) R/30 D) r/30

Conductors in Equilbirum A conductor has charges that can move freely In equilibrium the charges are not moving Therefore, there are no electric fields in a conductor in equilibrium = 0 = 0 The interior of a conductor never has any charge in it Charge on a conductor is always on the surface

Electric Fields near Conductors No electric field inside the conductor Electric field outside cannot be tangential – must be perpendicular Area A Add a gaussian pillbox that penetrates the surface Surface charge  Electric field points directly out from (or in to) conductor

Conductors shield charges Draw a Gaussian surface No electric field – no charge Inner charge is hidden – except No net charge Charge -q What is electric field outside the spherical conductor? Charge +q Charge q Charge +q on outside to compensate Charge distributed uniformly