Conductors

1. Conductors • Conductors contain charges capable of moving freely. Externally applied electric fields produce forces on the charge carriers (usually electrons) within the conductor, generating a current that rearranges the charges. Once the charges have rearranged so as to cancel the applied field inside, the current stops. Therefore, electrostatic potential inside conductor and on its surface is constant. • Conductor’s surface is equipotential • Tangential component of E vanishes • Any excess charge placed on a conductor must lie entirely on its surface • Electric field at the surface of a charged conductor

2. Faraday Cage A Faraday cage or Faraday shield is an enclosure formed by conducting material, or by a mesh of such material. Such an enclosure blocks out external static electrical fields. Faraday cages are named after Michael Faraday, who invented them in 1836. A Faraday cage's operation depends on the fact that an external static electrical field will cause the electrical charges within the cage's conducting material to redistribute themselves so as to cancel the field's effects in the cage's interior. This phenomenon is used, for example, to protect electronic equipment from lightning strikes and other electrostatic discharges. To a large degree, Faraday cages also shield the interior from external electromagnetic radiation if the conductor is thick enough and any holes are significantly smaller than the radiation's wavelength.

3. Example: Find the electric field of a spherical conductor of a positive charge +q

4. Example: An uncharged spherical conductor centered at the origin has a cavity of some weird shape carved out of it. Somewhere within the cavity is a charge q. What is the field outside the sphere? q (a) Charge on a solid conductor resides entirely on its outer surface. (b) If there is no charge inside the conductor's cavity, the net charge on the surface of the CAVITY is zero. (c) If there is a charge +q inside the cavity, the total charge on the cavity surface is -q.

5. Example: A positive point charge q is located near a conducting sphere. The sphere is electrically neutral. +q Which of the following statements is true: The charge and the sphere repel each other The charge and the sphere attract each other There is no interaction between the charge and the sphere • Example: A metal sphere of radius R carrying charge q is located inside a thick concentric metal shell (inner radius a, outer radius b) that carries no net charge. • Find the surface charge density at R, a, and b. • Find the potential at the center, using infinity as the reference point • Now the outer surface is touched to a grounding wire, which lowers its potential to zero. Will this change previous answers?