First page Back Continue Last page Overview Image
- PHY102 Physics II © Dr.Cem Özdoğan
- 23-9 Applying Gauss’Law: Spherical Symmetry
- Using Gauss’ law, it is easy to prove these shell theorems:
- 1- Applying Gauss’ law for spherical Gaussian surface S2 yields (r ≥ R)
- This field is the same as one set up by a point charge q at the center of the shell of charge. Thus, the force produced by a shell of charge q on a charged particle placed outside the shell is the same as the force produced by a point charge q located at the center of the shell.
- 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 (ST1).
- If a charged particle is located inside a shell of uniform charge, there is no net electrostatic force on the particle from the shell (ST2).
- 2- Applying Gauss’s law for spherical Gaussian surface S1 yields (r’ < R)
- because this Gaussian surface encloses no charge. Thus, if a charged particle were enclosed by the shell, the shell would exert no net electrostatic force on the particle.