Consider an electron gyrating in the magnetic field associated with a sunspot which has a magnetic field strength of 0.25 T. The typical temperature of a sunspot is 3500 K the equipartition equation for velocity v, temperature T and mass m of a particle, is, 3KBT m kB is Boltzmann's constant (1.38×10-23 J/K). a) The mass of the Sun is approximately 2 × 1030 kg. Use this information and the infor- mation given above to compute the acceleration g due to gravity at the surface of the Sun. b) Compute the drift velocity īg due to gravity for a proton and an electron located within a sunspot. c) Assuming a typical mass density of the Sun's photosphere of 10-3 kg/m³, compute the number density of protons and electrons in the photosphere (where sunspots reside) assuming that the Sun is comprised of pure ionized hydrogen.
Consider an electron gyrating in the magnetic field associated with a sunspot which has a magnetic field strength of 0.25 T. The typical temperature of a sunspot is 3500 K the equipartition equation for velocity v, temperature T and mass m of a particle, is, 3KBT m kB is Boltzmann's constant (1.38×10-23 J/K). a) The mass of the Sun is approximately 2 × 1030 kg. Use this information and the infor- mation given above to compute the acceleration g due to gravity at the surface of the Sun. b) Compute the drift velocity īg due to gravity for a proton and an electron located within a sunspot. c) Assuming a typical mass density of the Sun's photosphere of 10-3 kg/m³, compute the number density of protons and electrons in the photosphere (where sunspots reside) assuming that the Sun is comprised of pure ionized hydrogen.
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Transcribed Image Text:Consider an electron gyrating in the magnetic field associated with a sunspot which has a magnetic
field strength of 0.25 T.
The typical temperature of a sunspot is 3500 K
the equipartition equation for velocity v, temperature T and mass m of a particle, is,
3kgT
V =
m
kB is Boltzmann's constant (1.38×10–23
J/K).
a) The mass of the Sun is approximately 2 × 1030 kg. Use this information and the infor-
mation given above to compute the acceleration g due to gravity at the surface of the Sun.
b) Compute the drift velocity Ūg due to gravity for a proton and an electron located within a sunspot.
c) Assuming a typical mass density of the Sun's photosphere of 10-3 kg/m³, compute the number
density of protons and electrons in the photosphere (where sunspots reside) assuming that the Sun
is comprised of pure ionized hydrogen.
d) Calculate the total current density J (accounting for the contributions of both electrons and
tons) within sunspots. You may assume that you can treat the ensemble of particles as a fully-ionized
hydrogen gas
pro-
where
Ne and
np are the same for the electrons and the protons.
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a)
Let G, M, and R denote the universal gravitation constant, the Sun’s given mass, and its radius, respectively.
The gravitational acceleration (g) at the Sun’s surface may be calculated from its standard formula as follows:
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