Take the Sun's rotation rate seen from the Earth as and

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Fluid and magnetohydrodynamic description · Laboratory, industrial and space plasmas

Plasma Physics, Ch Magnetohydrodynamics: Ohm's law for a moving plasma, frozen flux and magnetic pressure

Problem

Take the Sun's rotation rate seen from the Earth as

\Omega_\odot = 2.7\times10^{-6}\,\mathrm{rad\,s^{-1}}

and

1\,\mathrm{AU} = 1.5\times10^{11}\,\mathrm{m}

, and treat the solar wind as steady, radial and confined to the equatorial plane, with its field frozen in. ((a)) Find the angle

\chi

between the field line and the radial direction at the orbit of Mars,

r = 1.52\,\mathrm{AU}

, for a wind speed

U = 400\,\mathrm{km\,s^{-1}}

. ((b)) Find

\chi

at the Earth's orbit,

r = 1\,\mathrm{AU}

, in a fast stream with

U = 750\,\mathrm{km\,s^{-1}}

. ((c)) At what distance, in astronomical units, does the field line of the

400\,\mathrm{km\,s^{-1}}

wind make an angle of

80^\circ

with the radial direction?

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