Read Back Signals in Magnetic Recording - Research Group Fidler

Basics
curl H = 0 . (2.15)
So H is a irrotational field and can therefore be expressed as gradient of a scalar field Ψ ,
called magnetic potential.
H =−grad Ψ
(2.16)
The magnetic potential of a volume V with a given magnetic polarization J can be calculated
by solving the Poisson equation
ρm
ΔΨ = − μ
with the jump condition
0
out in
∂Ψ ∂Ψ σ
− =−
∂n ∂n μ
∂V
m
0
(2.17)
(2.18)
at the boundary ∂ V . Here ρ m and σ m are magnetic charge densities in the volume V and at
its boundary ∂ V . These charges are only virtual, because there are no magnetic monopoles in
reality. These virtual charges are useful to calculate the magnetic potential of a polarization
distribution. They can be obtained by taking the divergence and the face divergence of the
magnetic polarization J.
ρ =−div J, σ =−Div
J (2.19)
m m
The face divergence is defined as difference of the normal components of outer and inner
field.
( )
out in out in
Div J = J −J ⋅ n = J −J
(2.20)
n n
Assuming that the magnetic potential is regular at infinity,
1
Ψ→ for r →∞, (2.21)
r
the solution of (2.17) and (2.18) is
1 ⎛ ρ σ ⎞
Ψ= dV + dA
4
∫ ∫� . (2.22)
m m
⎜ ⎟
πμ0 ⎝ r r
V ∂V
⎠
13