A planet has a liquid iron core of radius with electrical conductivity

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history

The Solid Earth, Ch The geomagnetic field: potential, spectrum, induction and the palaeomagnetic record

Problem

A planet has a liquid iron core of radius

r_{\rm c}=2000\,\mathrm{km}

with electrical conductivity

\sigma_e=5\times10^{5}\,\mathrm{S\,m^{-1}}

. Take

\mu_0=4\pi\times10^{-7}\,\mathrm{H\,m^{-1}}

and

1\,\mathrm{yr}=3.156\times10^{7}\,\mathrm{s}

. ((a)) Compute the magnetic diffusivity

\eta_m

and the magnetic diffusion time

\tau_d=r_{\rm c}^2/(\pi^2\eta_m)

of the core, in kyr. ((b)) Repeated surveys, continued down to the core surface, show a patch of radial flux drifting westward at

0.5^\circ\,\mathrm{yr^{-1}}

near the core's equator. Treating the flux as frozen in, infer the flow speed at the top of the core in

\mathrm{m\,s^{-1}}

. ((c)) How long does a patch

1000\,\mathrm{km}

across take to drift its own width, and is frozen flux a good approximation over that time?

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