Download - ELEC 3105 Lecture 1 Coulomb. 4. Electrostatics Applied EM by Ulaby, Michielssen and Ravaioli
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ELEC 3105 Lecture 1
Coulomb
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4. ElectrostaticsApplied EM by Ulaby, Michielssen and Ravaioli
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Chapter 4 Overview
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Maxwell’s Equations
God said:
And there was light!
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Current Density
For a surface with any orientation:
J is called the current density
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ELEC 3105 Lecture 1
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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
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Coulomb’s force law (point charges)q1
q2 F
origin
1r
2r
1212 rrr
122
12
2112 r
r
qkqF
[F]-force; Newtons {N}
[q]-charge; Coulomb {C}
[r]-distance; meters {m}
[]-permittivity; Farad/meter {F/m}
Property of the medium
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Coulomb’s force law (permittivity)
o
mediumr
Relative permittivity
omedium 0006.1For a medium like air
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Coulomb’s force law (permittivity)
omedium
122
12
2112 r
r
qkqF
medium
k41
FORCE IN MEDIUM SMALLER THAN FORCE IN VACUUM
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Lecture 1 (ELEC 3105)Basic E&M and Power
Engineering
Coulomb's LawThe 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
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Electric Field Due to 2 Charges
Example of (4.18) next
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Electric Field due to Multiple Charges
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Electric field (charge distribution)
x
y
z
q1
q2
P
N
i i
ii
rr
rrqkE
13
Large number N of point charges
q3
q4
q5
qN
qi
ir irr
r
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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
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Charge Distributions
Volume charge density:
Total Charge in a Volume
Surface and Line Charge Densities
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Electric Field Due to Charge Distributions
Field due to:
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Electric field (charge distribution)
qCharge always occurs in integer multiples of the electric charge e = 1.6X10-19C.
It is often useful to imagine that there is a continuous distribution of charge
Charged volume
Charged surface
Charged line
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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
V Volume charge density
V Units; {C/m3 }
dVV Charge in dV
When the volume element dV--> 0
Sum --> Integral
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Electric field (charge distribution)
Charged volume
P
VdV r
Ed
V
Field for one element
2r
kdqrEd
dVdq VWith
2r
dVkrEd V
Integration overvolume V
V
V
V r
dVkrEdE 2
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Electric field (charge distribution)
V
V
V r
dVkrEdE 2
,.....dxdydzdV
,....222 zyxr
V may be a function of the coordinates usually a constant
41
k usually a constant when medium is uniform
unit vectorfunction of (x,y,z),….
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Electric field (charge distribution)
The electric field produced at the point P is:
Charged surface
Charge surface element dS
s Surface charge density
s Units; {C/m2}
dSs Charge on dS
P
S
s
S r
dSkrEdE 2
q
dS
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Electric field (charge distribution)
,.....dxdydS
,....222 zyxr
s may be a function of the coordinates usually a constant
41
k usually a constant when medium is uniform
unit vectorfunction of (x,y,z),….
S
s
S r
dSkrEdE 2
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Electric field (charge distribution)
The electric field produced at the point P is:
Charged line element d
Linear charge density
Units; {C/m}
d Charge on
P
LL r
dkrEdE 2
Charged line
q
d
d
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Electric field (charge distribution)
,.....dxd
,....222 zyxr
may be a function of the coordinates usually a constant
41
k usually a constant when medium is uniform
unit vectorfunction of (x,y,z),….
LL r
dkrEdE 2
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Cont.
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Cont.
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Example 4-5 cont.
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