Electric field of single point charge kq1 q ˆˆ E =22 r = r rr4 0 Surface area of a sphere: A = 4 r2 Gauss’ Law • The total electric flux (i.e. # of field lines) leaving a Gaussian (closed) surface is proportional to the charge enclosed by that surface. Gaussian Surface • A surface that encloses a volume. – It separates space into an inside and an outside. – You cannot get from the inside to the outside without going through the surface. Electric Flux • A quantitative measure of the number of field lines through a surface. – Depends on the magnitude of the electric field. – Depends on the area of the surface. Flux when field is not perpendicular to surface. EAcos Figure 22.1c E Electric Flux (for flat surface and uniform field) E EAcos EAcos Enˆ A nˆ - unit vector that points perpendicular (normal) to surface. - two possible directions for most surfaces; ambiguity. - for Gaussian surfaces, n points out, by convention. Figure 22.2 Electric Flux (for any surface and any field) EnˆdA E nˆ - unit vector that points perpendicular (normal) to surface. - two possible directions for most surfaces; ambiguity. - for Gaussian surfaces, n points out, by convention. A positive point charge q resides at the center of a spherical Gaussian surface of radius r. What is E·n at the surface? 1) kq/r2 2) -kq/r2 3) kq/(√2r2) 4) 0 5) It depends on which particular point on the surface we are considering. A positive point charge q resides at the center of a spherical Gaussian surface of radius r. What is the total flux through the surface? 1) 4πkq/r2 2) q/ε0 2 3) 4πr q/ε0 4) 0 5) It depends on the color of the sphere. A positive point charge q resides at the center of a spherical Gaussian surface of radius r. The surface is deformed so that it has an outward pointing pyramidal dimple. How does the total flux through the surface change? 1) It increases. 2) It decreases. 3) It doesn’t change. 4) It depends. Figure 22.10 Gauss’ Law • The total electric flux (i.e. # of field lines) leaving a Gaussian (closed) surface is proportional to the charge enclosed by that surface. Q net Enˆ dA encl E 0 Gauss’ Law and Symmetry • You can use Gauss’ Law to calculate electric fields when the situation has some symmetry: – When symmetry determines the direction of E, and/or – When it determines how E depends on some coordinate. • Choose your Gaussian surface to exploit the symmetry so that E = 0 or is otherwise easy to calculate on some parts of the surface. Spherical shell of charge Figure 22.11 Inside spherical shell of charge Figure 22.11.