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Gauss’s Law Electric Flux • Measure of the number of electric field lines passing through a surface. • For a uniform electric field E A E A cos • Non-uniform electric field E dA surface Calculate Flux • A square with an area of 5 m² has a surface normal of 1 5 iˆ 2 5 ˆj. What is the flux through this surface if the square is embedded in a uniform electric field of 6.0 ˆjN / C ? Closed Surface • Consider the flux on a closed surface. Tp Lf Bk Rt Fr Bt total Fr Bk Lf Rt Tp Bt 0 Gauss’ Law • Net electric flux through any closed gaussian surface is equal to the net charge inside divided by e0. qin E E dA e0 Point Charge • Choose a sphere as your gaussian surface. • Electric field is perpendicular to the surface and of uniform strength at the surface. 2 E dA E 4r q 2 E 4r e0 q or E k 2 r q Line Charge • Choose a cylinder as your gaussian surface. • Electric field is perpendicular to the walls and parallel to the end caps. Fr Bk Wall q E 2rl e0 q or E 2k 2k lr r Sheet Charge • Choose a box as your gaussian surface. • Electric field is perpendicular to the top & bottom, but parallel to the sides. Lf Rt Fr Bk Tp Bt EA EA q e0 q or E 2 Ae 0 2e 0 Volume Charge • Choose a sphere as your gaussian surface. • Gaussian surface may be inside the volume. E 4r 3 4 qin 3 r 2 E r 3e 0 q Conductors • Electric field is zero inside a conductor • Any excess charge must be on the surface • Electric field leaves perpendicular to the surface. • Irregular shapes: more charge accumulates where the radius of curvature is smallest. • Near the surface E e0 Irregular Conductors • How would you draw the electric field on the following conductors?