Gausss Law The net electric flux through any
- Slides: 9
Gauss’s Law “The net electric flux through any closed surface is directly proportional to the net charge contained within that surface. ” Qenclosed = e 0(FE) 4/17/19 OSU PH 213, Before Class #8 1
This box contains A. B. C. D. E. 4/17/19 a net positive charge. a net negative charge. a positive charge. no net charge. OSU PH 213, Before Class #8 2
This box contains A. B. C. D. E. 4/17/19 a net positive charge. a net negative charge. a positive charge. no net charge. OSU PH 213, Before Class #8 3
These are two-dimensional cross sections through three-dimensional closed spheres and a cube. Rank order, from largest to smallest, the electric fluxes a to e through surfaces a to e. A. B. C. D. E. 4/17/19 Φa > Φ c > Φ b > Φ d > Φ e Φb = Φ e > Φ a = Φ c = Φ d Φe > Φ d > Φ b > Φ c > Φ a Φb > Φ a > Φ c > Φ e > Φ d Φd = Φ e > Φ c > Φ a = Φ b OSU PH 213, Before Class #8 4
These are two-dimensional cross sections through three-dimensional closed spheres and a cube. Rank order, from largest to smallest, the electric fluxes a to e through surfaces a to e. A. B. C. D. E. 4/17/19 Φa > Φ c > Φ b > Φ d > Φ e Φb = Φ e > Φ a = Φ c = Φ d Φe > Φ d > Φ b > Φ c > Φ a Φb > Φ a > Φ c > Φ e > Φ d Φd = Φ e > Φ c > Φ a = Φ b OSU PH 213, Before Class #8 5
An electrically neutral cylindrical piece of material is placed in an external electric field, as shown. The net electric flux through the surface of the cylinder is… 1. positive. 2. negative. 3. zero. 4/17/19 OSU PH 213, Before Class #8 6
An electrically neutral cylindrical piece of material is placed in an external electric field, as shown. The net electric flux through the surface of the cylinder is… 1. positive. 2. negative. 3. zero. 4/17/19 OSU PH 213, Before Class #8 7
So, when is Gauss’s Law useful? When we already know the shape/form of the E-field (but not necessarily its magnitude)—and that form is symmetric and/or uniform, so that we can avoid nasty surface integrals by selecting certain simple Gaussian surfaces: A spherical surface (for spherically symmetric charge distributions), as shown on the next slide. A cylindrical surface (for very long lines/cylinders of cylindrically symmetric charge distributions). A rectangular “box” surface (for very large planes of rectangular symmetric charge distributions). In Class 8, we will look at simple examples of each kind of charge distribution; and After Class 8 will follow with other examples. 4/17/19 OSU PH 213, Before Class #8 8
4/17/19 OSU PH 213, Before Class #8 9
