A plane isothermal atmosphere at temperature T is in a uniform gravitational field with accel- eration g in the negative z direction. Show that the density in hydrostatic equilibrium, in the absence of a magnetic field, is given by p(z) = Poe-z/H where H = RT/µg, µ is the mean molecular weight and po is the density at z = 0. Find p(z) when the isothermal gas is a fully ionised plasma with a magnetic field B = (B(2), 0, 0) where B(z)= Bo(p/po) ¹/2.
A plane isothermal atmosphere at temperature T is in a uniform gravitational field with accel- eration g in the negative z direction. Show that the density in hydrostatic equilibrium, in the absence of a magnetic field, is given by p(z) = Poe-z/H where H = RT/µg, µ is the mean molecular weight and po is the density at z = 0. Find p(z) when the isothermal gas is a fully ionised plasma with a magnetic field B = (B(2), 0, 0) where B(z)= Bo(p/po) ¹/2.
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![A plane isothermal atmosphere at temperature T is in a uniform gravitational field with accel-
eration g in the negative z direction. Show that the density in hydrostatic equilibrium, in the
absence of a magnetic field, is given by
p(2) = Poe-/H
where H
= RT/µg, µ is the mean molecular weight and po is the density at z = 0. Find p(z)
when the isothermal gas is a fully ionised plasma with a magnetic field B = (B(2), 0,0) where
B(2) = Bo(p/po)/2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18992c9e-8ff4-49dd-8142-d6d4d5747fdb%2F3d6a6a8f-949c-4619-be5b-bed5d6a50f50%2F2gr593a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A plane isothermal atmosphere at temperature T is in a uniform gravitational field with accel-
eration g in the negative z direction. Show that the density in hydrostatic equilibrium, in the
absence of a magnetic field, is given by
p(2) = Poe-/H
where H
= RT/µg, µ is the mean molecular weight and po is the density at z = 0. Find p(z)
when the isothermal gas is a fully ionised plasma with a magnetic field B = (B(2), 0,0) where
B(2) = Bo(p/po)/2.
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