E-M field
THz
Formula for E-M field
Maxwell Equations:
rr D Gausss law: E rr Gausss law: M B 0 rr r Faraday's law E B t r r r r Ampere Maxwells law H J D t
Scalar & Vector
A scalar is a quantity that has only magnitude A vector is a qua
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Vectors&VectorCalculus
Vectors&Scalars
Ascalar isaquantitythathasonlymagnitude.
e.g.temperature,pressure,length,voltage,mass
Avector isquantitythathasbothmagnitudeanddirection
e.g.velocity,force,acceleration,electricfield
vy
v v xa x v ya y vz
Vector Multiplication
Scalar (or dot) product
rr r r A B A B cos AB rr A B A x Bx A y By A z Bz
Rules:
rr rr Commutative: A B B A rrr rr rr Distributive: A (B C) A B A C r r r2 Find magnitude of a vector: A A A
Some simple identities
a x
Resistor and Capacity
s Resistor: E
rr V E dl r R r I E dS
s
(+)
(-)
Capacitance
rr Q s E dS r r C V E dl
s E (1) (2)
Energy of Cap:
1 1 Q2 2 W C V V Q 2 2 2C
Calculate capacitance
Let two conductor carry charge +Q and Q, respecti
Electrostatic boundary value problem
Deriving Poissons equation:
r r D E v E V
2
Gausss law
Poissons equation for electrostatics:
V v /
Laplaces equation:
v 0
V0
2
Laplace operator
Cartesian:
2V 2V 2V V 2 2 2 x y z
2
Cylindrica
HW1 solution
Find electric field, displacement, and potential r=4 v=1c/m3 Approach: r=2 R2=0.5m R1=1m
Step 1: Use Gausss law to solve the displacement vector Step 2: Use the displacement vector to find the electric field Step 3: Integrate the electr
E-field in different materials
Conductor Insulator Semi-conductor
Current and current density
Current:
Current density: (assuming the current is perpendicular to dS)
dQ I= dt
dI j= dS Relation between current and current density
I = j dS
S
Electric potential
Differential work
Work needed to move charge from A to B
Potential difference between A and B
Absolute potential
Unless otherwise specified, we assume zero potential point is at inf! Absolute potential at an arbitrary point A:
EX 4.5
The finite sheet 0<x<1, and 0<y<1 on the z=0 plane has a charge density
s = xy ( x 2 + y 2 + 25)3 / 2 nC / m 2
Find:
(a). The total charge on the sheet (b). The electric field at (0,0,5) (c). The force experienced by a 1-mC charge located
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ElectrostaticFields
MaxwellsEquations
D v
B 0
B
E
t
E 0
StaticFields
D
H J
t
H J
1
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ElectricCharge
FARADAY
Theelectricchargeisthefundamentalpropertyof
matterwhichgenerateselectrostaticfields
Theelementarychargeis1.6021019C,whi