Read Back Signals in Magnetic Recording - Research Group Fidler

2 BasicsEquation
Section (Next)
2.1 Ohm’s Law
Basics
Georg Simon Ohm (1789-1854) found that the current I through most materials is
proportional to the applied voltage V.
V = R⋅ I
(2.1)
The proportional coefficient is called resistance R. The more general form of this equation is
shown below.
σ⋅ E = j (2.2)
E [V/m] denotes the electric field, and j [A/m 2 ] the current density. σ [A/Vm] is a property
of matter named conductivity. Generally the conductivity is a tensor, but here all conductors
will be assumed to be isotropic.
2.2 Maxwell’s Equations
James Clerk Maxwell (1831-1879) was the first who joined the theories of electricity and
magnetism. He proposed following four equations to describe both theories (in SI).
� ∫ DdA= ∫ρdV
(2.3)
∂V
V
� ∫ BdA= 0
(2.4)
∂V
∂
� ∫Eds=− d
∂t
∫B
A
(2.5)
∂A
A
∂
� ∫ Hds= ∫jdA+ d
∂t
∫D
A
(2.6)
∂A
A A
These four integral equations can also be written as equivalent differential equations.
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