EECE 380 Notes, Spring 2008

Main concepts in Electrostatics Maxwell’s equation for electrostatics: Where D: Electric field density (N/m) E: Electric field intensity (N/m) Force acting on a point charge exposed to an electric field: F=qE (N) Charge calculation: The total charge contained in a given volume is given by For a surface charge distribution: For a line charge distribution: Coulomb’s law to get the electric field due to a charge distribution: Volume charge distribution: Surface charge distribution: Line charge distribution: Examples:  Discrete charges:  Infinitely long line:  Infinite sheet: (for a point above the sheet and the opposite for a point below it) For the following cases, all charge distributions are on the xy plane and we are considering E at P(0,0,h)  Circular ring:  Ring with inner radius a and outer radius b:  Disk of radius a : Gauss’s law to get the electric field due to a charge distribution: Electric scalar potential: By taking P1 at infinity, Electric field as a function of electric potential Electric potential in Boundary value problem: Electric polarization vector: P=ε0 χ E So D= ε0E+P= ε0(1+ χ)E where εr= χ +1 Calculation of the resistance: Procedure that can be useful for calculating the resistance of a conductor in many cases: 1- Choose an appropriate coordinate system for the geometry. 2- Assume a potential difference Vo between the conductor terminals. 3- Find E within the conductor. 4- Find the total current as 5- Find the resistance as in Ω Conductance: G=1/R in Siemens (S) Calculation of the capacitance: Procedure for calculating the capacitance in many cases: 1- Choose an appropriate coordinate system. 2- Assume +Q and –Q on the conductor. 3- Find E from Q using Gauss law or other relations. 4- Find V: V= 5- C= Examples:  Parallel plate capacitor: C= εS/d  Cylindrical capacitor: C= 2πεL/ln(b/a) Electrostatic energy: And Q=CV For discrete charges, Electrostatic Force: Material characteristic: Electric Boundary conditions: Consider,  For a perfect conductor, Parameters: