Phys math help.pdf


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Energy of magnetic field
δW = I.δφ
Z
1
d3 x.B 2
2µ0
Z
1
~A
~
W =
d3 x.J.
2

W =

2

(12)
(13)
(14)

Maxwell Equations
~ E
~ = ρ
∇.
0
~
~ ×B
~ − µ0 0 ∂ E = µ0 J~

∂t
~
~ ×E
~ + ∂B = 0

∂t
~
~
∇.B = 0

Conservation law

(I)
(II)
(III)
(IV)

∂ρ ~ ~
+ ∇.J = 0
∂t

(15)

~ =∇
~ ×A
~
B

(16)

~
~ = −∇ϕ
~ − ∂A
E
∂t

(17)

Potentials

Relativistic form

1 ν
j
c 0

3

∂µ F µν =


with F µν

0
 E1
=
 E2
E3

−E 1
0
cB 3
−cB 2

−E 2
−cB 3
0
cB 1

−E
cB 2 
~
 and j µ = (cρ, J)
−cB 1 
0

2

(18)