Maxwell's equations of electromagnetism
 
div

D
 
= ρ
Gauss' Law for electricity
scalar sources of electric fields
electric charges produces electric fields
 
div

B
 
= 0
Gauss' Law for magnetism
scalar sources of magnetic fields
no magnetic monopoles
 
curl

E
 
= -
δ
 

B

δ t
Faraday's Law of induction
vectorial sources of electric fields
changing magnetic fields produce electric fields
 
curl

H
 
=

J +
δ
 

D

δ t
Ampère's Law
vectorial sources of magnetic fields
electric currents and changing electric fields produces magnetic fields


D
 
= ε

E

B
 
= μ

H

 
div

D
 
=
 

D
 
curl

E
 
=
 
x

E
 
div =
 
divergence =
 
 
=
 
del or nabla operator
 

 
= δ

δ x

i
 
+ δ

δ y

j
 
+ δ

δ z

k
 

 
curl =
 
curl or rotation =
 
 
x =
 
curl operator
 
x

E
 
=


i
 

j
 

k
 
δ / δ xδ / δ yδ / δ z
ExEyEz


D is the electric displacement field

E
 
is the electric field

J
 
is the current density
ρ is the electric charge density
ε is the electrical permittivity of the material
 

H
 
is the magnetic field intensity or magnetic field strength

B
 
is the magnetic field or magnetic induction
μ is the magnetic permeability of the material


Maxwell equations
in vacuum
 
div

D
 
= 0
 
div

B
 
= 0
 
curl

E
 
= -
δ
 

B

δ t
 
curl

H
 
=
δ
 

D

δ t