Energy Density of a Magnetic Dipole
Energy Density of a Magnetic Dipole
A circular conductor with the current and the radius lies in the plane at . The vector potential in the direction as a function of and has the same symmetry as the current density in cylindrical coordinates , , . According to the cylindrical symmetry the observation points in the plane can be taken at . The source is described by the angle , running from to . The following computations are made: • the magnetic field in the direction• the magnetic field in the direction• the magnetic energy density • the integrated magnetic field in the direction• the integrated magnetic field in the direction• the integrated magnetic energy density • the integrated vector potential in the directionThe fields at can be regarded as a good approximation of the integrated fields. The four field , , , are displayed for the four independent variables , , , . The observation points are described by , and the source by , .
I
1
R
x-y
z=0
Aϕ(ρ,z,R,α)
ϕ
ρ
z
ρ
ϕ
z
x-z
ϕ=0
α
0
2π
Bρ(ρ,z,R,α)
ρ
Bz(ρ,z,R,α)
z
u(ρ,z,R,α)
Bρ(ρ,z,R)
ρ
Bz(ρ,z,R)
z
u(ρ,z,R)
Aϕ(ρ,z,R)
ϕ
α=0
A ϕ
B ρ
B z
u
ρ
z
R
α
ρ
z
R
α