Electromagnetic Fields – Main Results

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PHY2206 (Electromagnetic Fields) Fundamental Results
1
Electromagnetic Fields Ð Main Results
Symbols
MISCELLANEOUS
c ms
Ð1
Velocity of light in free space
r m Position vector
d
3

r m
3
Differential volume element
dV m
3
Differential volume element

0
Fm
Ð1
Permittivity of free space

0
Hm
Ð1
Permeability of free space
PROPERTIES OF AN ENTITY OR SYSTEM
C F Capacitance
I A Electric current
L H Inductance
m Am
2
Magnetic dipole moment
p Cm Electric dipole moment
q C Electric charge
t s Time
U J Potential energy of a system

r
Relative permittivity

r
Relative permeability

Susceptibility
FIELDS
A Tm Magnetic vector potential
B T Magnetic induction field, (aka
magnetic flux density)
D Cm
Ð2
Electric displacement field
E Vm
Ð1
Electric field
F N Force
H Am
Ð1
Magnetic field intensity
M JT
Ð1
m
Ð3
Magnetisation field
P Cm
Ð2
Electric polarisation field
j Am
Ð2
Current density
j
c
Am
Ð2
Conduction current density
j
M
Am
Ð2
Magnetisation current density

Cm
Ð3
Electric charge density

f
Cm
Ð3
Free charge density

b
Cm
Ð3
Bound charge density

Cm
Ð2
Surface charge density

V Electric potential
PHY2206 (Electromagnetic Fields) Fundamental Results
2
© Copyright CDH Williams
Exeter 1997, CW970606/3
Fundamental Results
Static Systems General Systems
F
12
=
q
1
q
2
4

0
r 

r
( )
r 

r
3
F = q E+ v  B
( )
E r
( )
=
 
r
( )
.
r 

r
( )
d
3

r
4

0
r 

r
3



 × E
( )
=


0
E = 

E = 
 
 A
 t
  E = 0
  E = 
 B
 t
 × j
( )
+


 t
= 0
  B
( )
=

0
j
  B
( )
=

0
j +
1
c
2
 E
 t
B r
( )
=

0
4

j

r
( )

r 

r
( )
d
3

r
r 

r
3



 × B
( )
= 0
  A = B

2

= 


0

2


1
c
2

2

 t
2
= 


0

2
A =  
0
j 
2
A
1
c
2

2
A
 t
2
=  
0
j
 × A
( )
= 0  × A+
1
c
2

2

 t
2
= 0
U =
1
2

+ j×A
( )

d
3
r U =
1
2

0
E
2
+ B
2

0
( )

d
3
r