Physics 121: Electricity & Magnetism – Lecture 5 Carsten Denker NJIT Physics Department Center for Solar–Terrestrial Research

February 14, 2007Center for Solar-Terrestrial Research Capacitance Capacitance [F = C/V] A battery maintains a potential difference V between its terminals. It sets up an electric field which drives electrons through the wire towards the positive terminal.

February 14, 2007Center for Solar-Terrestrial Research Calculating the Capacitance Parallel-plate capacitor Cylindrical capacitor Spherical capacitor Isolated sphere

February 14, 2007Center for Solar-Terrestrial Research Capacitors in Parallel & in Series n capacitor in parallel n capacitors in series When a potential difference V is applied across several capacitors connected in parallel, that potential difference V is applied across each capacitor. The total charge q stored on the capacitors is the sum of the charges stored on all the capacitors. When a potential difference V is applied across several capacitors connected in series, the capacitors have identical charges q. The sum of the potential differences across all the capacitors is equal to the applied potential difference V.

February 14, 2007Center for Solar-Terrestrial Research Energy Stored in an Electric Field Potential energy Energy density The potential energy of a charged capacitor may be viewed as being stored in the electric field between its plates. Material Dielectric Constant  Dielectric Strength (kV/mm) Air Polystyrene2.624 Paper3.516 Transformer Oil4.5 Pyrex4.714 Ruby Mica5.4 Porcelain6.5 Silicon12 Germanium16 Ethanol25 Water (20º C)80.4 Water (50º C)78.5 Titania Ceramic130 Strontium Titanate3108

February 14, 2007Center for Solar-Terrestrial Research Capacitor with a Dielectric In a region completely filled by a dielectric material of dielectric constant , all electrostatic equations containing the permittivity constant  0 are to be modified by replacing  0 with   0. Polar and non- polar dielectrics Gauss’ law with dielectric