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.