A Brief Introduction to Space Plasma Physics.pdf - Institute of ...

• Maxwell’s equations in integral form
r 1
∫ E ⋅ ndA ˆ = ∫ ρ dV
A
ε 0
– A is the area, dA is the differential element of area
– nˆ is a unit normal vector to dA pointing outward.
– V is the volume, dV is the differential volume element
ˆn '
∫
∫
A
C
r
B ⋅ nd ˆ A =
v r
E ⋅ ds = −
0
r
∂B
∂t
'
⋅nˆ
dF = −
∂Φ
∂ t
– is a unit normal vector to the surface element dF in the
direction given by the right hand rule for integration around
C, and is magnetic flux through the surface.
ds
r
Φ
– is the differential element
r
around C.
r r ∂E
'
∫ B ⋅ds
= 2 n dF J
C
c ∫ ⋅ ˆ + µ
0
∂t
∫
∫
1
ˆ
'
⋅n dF