ELEC 3105 Lecture 1 Coulomb.

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Presentation transcript:

ELEC 3105 Lecture 1 Coulomb

Applied EM by Ulaby, Michielssen and Ravaioli 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

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) q1 q2 [F]-force; Newtons {N} [q]-charge; Coulomb {C} [r]-distance; meters {m} []-permittivity; Farad/meter {F/m} origin Property of the medium

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

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) q1 q3 qi z P q2 q4 qN y Large number N of point charges x q5

PRINCIPLE OF SUPERPOSITION 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.

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

Electric Field Due to Charge Distributions

Electric field (charge distribution) Charge always occurs in integer multiples of the electric charge e = 1.6X10-19C. Charged volume q Charged surface It is often useful to imagine that there is a continuous distribution of charge Charged line

Electric field (charge distribution) P Charge volume element dV q Volume charge density Units; {C/m3 } Charged volume Charge in dV The electric field at the point P is obtained by summing the electric field contribution from from each volume element dV. When the volume element dV--> 0 Sum --> Integral

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

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

Electric field (charge distribution) P Charge surface element dS dS Surface charge density q Units; {C/m2} Charged surface Charge on dS The electric field produced at the point P is:

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

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

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

Cont.

Cont.

Example 4-5 cont.