In a quiet period

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Plasma Physics · The plasma state and single-particle motion

Plasma Physics, Ch One particle in given fields: gyration and the guiding-centre drifts

Problem

In a quiet period, protons of energy

W = 50\,\mathrm{keV}

fill a ring around the Earth near the

L = 4

shell, at equatorial distance

r = 4R_E

with

R_E = 6371\,\mathrm{km}

, where the equatorial field is

B = B_0/L^3

with

B_0 = 3.12\times10^{-5}\,\mathrm{T}

. Take every proton to move perpendicular to the field at the equator, and take their density as

n = 1.0\times10^{6}\,\mathrm{m^{-3}}

, spread uniformly over a ring of square cross-section

2R_E \times 2R_E

. Count only the drift current

\sum_sn_sq_s\mathbf{v}_{ds}

of the protons. ((a)) Find the protons' drift speed and say which way they drift. Electrons of the same energy drift at the same speed; say whether their current adds to the protons' or cancels it. ((b)) Find the drift current density and the total current

I

the ring carries. ((c)) Treat the ring as a single circular loop of radius

r

, whose field at its centre is

\mu_0I/2r

. Find the size and direction of the field change at the Earth, and the factor by which the proton density would have to rise to give the

589\,\mathrm{nT}

depression of March 1989.

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