ELEC 3105 Lecture 1 Coulomb

4. Electrostatics Applied EM by Ulaby, Michielssen and Ravaioli

Chapter 4 Overview

Maxwell’s Equations God said: And there was light!

Current Density For a surface with any orientation: J is called the current density

Convection vs. Conduction

ELEC 3105 Lecture 1

Coulomb’s Law Electric field at point P due to single charge Electric force on a test charge placed at P Electric flux density D

Coulomb’s force law (point charges) q1q1 q2q2 origin [F]-force; Newtons {N} [q]-charge; Coulomb {C} [r]-distance; meters {m} [  ]-permittivity; Farad/meter {F/m} Property of the medium

Coulomb’s force law (permittivity) Relative permittivity For a medium like air

Coulomb’s force law (permittivity) FORCE IN MEDIUM SMALLER THAN FORCE IN VACUUM

Lecture 1 (ELEC 3105) Basic E&M and Power Engineering Coulomb's Law The force exerted by one point charge on another acts along the line joining the charges. It varies inversely as the square of the distance separating the charges and is proportional to the product of the charges. The force is repulsive if the charges have the same sign and attractive if the charges have opposite signs. Action at a distance

Electric Field Due to 2 Charges Example of (4.18) next

Electric Field due to Multiple Charges

Electric field (charge distribution) x y z q1q1 q2q2 P Large number N of point charges q3q3 q4q4 q5q5 qNqN qiqi

Given a group of charges we find the net electric field at any point in space by using the principle of superposition. This is a general principle that says a net effect is the sum of the individual effects. Here, the principle means that we first compute the electric field at the point in space due to each of the charges, in turn. We then find the net electric field by adding these electric fields vectorially, as usual. PRINCIPLE OF SUPERPOSITION

Charge Distributions Volume charge density: Total Charge in a Volume Surface and Line Charge Densities

Electric Field Due to Charge Distributions Field due to:

Electric field (charge distribution) q Charge always occurs in integer multiples of the electric charge e = 1.6X C. It is often useful to imagine that there is a continuous distribution of charge Charged volume Charged surface Charged line

Electric field (charge distribution) q The electric field at the point P is obtained by summing the electric field contribution from from each volume element dV. Charged volume P Charge volume element dV Volume charge density Units; {C/m 3 } Charge in dV When the volume element dV--> 0 Sum --> Integral

Electric field (charge distribution) Charged volume P V Field for one element With Integration over volume V

Electric field (charge distribution)  V may be a function of the coordinates usually a constant usually a constant when medium is uniform unit vector function of (x,y,z),….

Electric field (charge distribution) The electric field produced at the point P is: Charged surface Charge surface element dS Surface charge density Units; {C/m 2 } Charge on dS P q dS

Electric field (charge distribution)  s may be a function of the coordinates usually a constant usually a constant when medium is uniform unit vector function of (x,y,z),….

Electric field (charge distribution) The electric field produced at the point P is: Charged line element d Linear charge density Units; {C/m} Charge on P Charged line q

Electric field (charge distribution) may be a function of the coordinates usually a constant usually a constant when medium is uniform unit vector function of (x,y,z),….

Cont.

Example 4-5 cont.