The current density J through the cross section of the neuronal projection could
be calculated from:
(74)
——
J=
——
ia
S
∂ V 1 = E 1 = 0.57V. m ~1
∂l ' RA ' RA 1Ωm
≈ 0.57A/m2
Magnetic field in dendrites
The currents inside dendrites are experimentally measured to be from 20pA to
100pA for GABAergic synapses (Akaike & Moorhouse, 2003). Using the formula
(75) <j) H ∙ dl = i
Γ
we can find the magnetic intensity for a contour Γ with length l=πd that
interweaves the whole current iA. For dendrite with d~1 μm we obtain:
(76)
H=
100 × 10-12A
3.14 × 10-6m
= 31.8 × 10-6 A.m-1
If we consider that the water and the microtubules form a system augmenting the
magnetic strength known as ferrofluid (Frick et al., 2003) then in the best-case
with effective magnetic permeability μeff ≈ 10, where μeff = —, we will obtain
μ0
the maximal magnitude of the magnetic induction B inside the neuronal
projection:
(77) B = μα μα H
(78) B=10×4π×10-7H.m-1×31.8×10-6A.m-1≈4×10-10T
44
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