Notes 2 ECE 2317 Applied Electricity and Magnetism Prof. D. Wilton ECE Dept. Charge! Notes 2 Notes prepared by the EM group, University of Houston.

Statics Definitions: Statics – frequency f = 0 [Hz] Quasi-statics – slow time variation, f << ? [Hz] The electromagnetic field splits into two independent parts: Electrostatics: (q, E) Static charge Magnetostatics: (I, B) Constant current w.r.t. time

Statics (cont.) Example: circuit

Statics (cont.) c = 2.99792458  108 [m/s] Example: f = 60 [Hz] 0 = c / f c = 2.99792458  108 [m/s] f = 60 [Hz] This gives: 0 = 4.9965106 [m] = 4,996.5 [km] = 3,097.8 [miles] Clearly, most circuits fall into the static-approximation category at 60 [Hz]!

Statics (cont.) The following rely on electro(quasi-)static and magneto(quasi-)static field theory: circuit theory (e.g, ECE 2300) electronics power engineering magnetics ECE 2317 Examples of high-frequency systems that are not modeled by statics: antennas transmission lines microwaves optics ECE 3317

Charge Ben Franklin electron: q = e = -1.602 x 10-19 [C] proton: q = -e = +1.602 x 10-19 [C] 1 [C] = 1 / 1.602 x10-19 protons = 6.242 x 1018 protons atom e p Ben Franklin

Charge Density v V Q 1) Volume charge density v [C/m3] uniform cloud of charge density

Charge Density (cont.) dV dQ non-uniform (inhomogeneous) volume charge density v (x,y,z) dV dQ non-uniform cloud of charge density

Charge Density (cont.) so v (x,y,z) dV dQ or

Charge Density (cont.) S Q 2) Surface charge density s [C/m2] s (x,y,z) S non-uniform sheet of charge density Q non-uniform uniform

Charge Density (cont.) s (x,y,z) dQ dS

Charge Density (cont.) l + Q 3) Line charge density l [C/m] l (x,y,z) Q l + non-uniform line charge density non-uniform uniform

Charge Density (cont.) l (x,y,z) dQ dl +

Example – Find the total charge in the spherical distribution z v = 10 [C/m3] a y x Find: Q

Example – Find the total charge in the non-uniform spherical distribution z v = 2r [C/m3] a y r Find: Q x

Example – Find the Equivalent Surface Charge Density for a Thin Slab of Charge z

Example – Find the Equivalent Line Charge Density for a Thin Cylinder of Charge z

Summary of Conversion to Equivalent Charge Densities Slab lying in a constant z-plane: Cylinder lying parallel to the z-axis: