# 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