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4. (a) The average magnetic field in the interstellar space of our galaxy is approximately 3 ! 10?? T. If the galaxy is taken to be a disk-shaped volume, of diameter 10²¹ m and thickness 10¹? m, what is the total magnetic energy of the galaxy? The total power radiated from all stars in the galaxy is about 10³? W. How many years of starlight are equivalent to the stored magnetic energy? (b) The magnetic field at the surface of a neutron star, or pulsar, is about 10? T. What is the magnetic energy density for this field? Using the mass-energy relation E = mc², find the mass density that corresponds to the magnetic energy density. Compare this to the mass density of the neutron star, assuming it has the mass of the sun in a sphere of radius 10 km. (c) Again, assume the magnetic field of the Earth in the region outside the Earth is a pure dipole field corresponding to a dipole moment m = 8 ! 10²² J/T (this is not completely accurate, because the solar wind cuts off the field at a distance of order 10 Earth radii, but it is a good approximation for this exercise). Calculate the total energy of the magnetic field outside the Earth. Compare the result to the rotational kinetic energy of the Earth.

          4. (a) The average magnetic field in the interstellar space of our galaxy is approximately 3 ! 10?? T. If the galaxy is taken to be a disk-shaped volume, of diameter 10²¹ m and thickness 10¹? m, what is the total magnetic energy of the galaxy? The total power radiated from all stars in the galaxy is about 10³? W. How many years of starlight are equivalent to the stored magnetic energy?
(b) The magnetic field at the surface of a neutron star, or pulsar, is about 10? T. What is the magnetic energy density for this field? Using the mass-energy relation E = mc², find the mass density that corresponds to the magnetic energy density. Compare this to the mass density of the neutron star, assuming it has the mass of the sun in a sphere of radius 10 km.
(c) Again, assume the magnetic field of the Earth in the region outside the Earth is a pure dipole field corresponding to a dipole moment m = 8 ! 10²² J/T (this is not completely accurate, because the solar wind cuts off the field at a distance of order 10 Earth radii, but it is a good approximation for this exercise). Calculate the total energy of the magnetic field outside the Earth. Compare the result to the rotational kinetic energy of the Earth.

4. (a) The average magnetic field in the interstellar space of our galaxy is approximately 3 ! 10?? T. If the galaxy is taken to be a disk-shaped volume, of diameter 10²¹ m and thickness 10¹? m, what is the total magnetic energy of the galaxy? The total power radiated from all stars in the galaxy is about 10³? W. How many years of starlight are equivalent to the stored magnetic energy?
(b) The magnetic field at the surface of a neutron star, or pulsar, is about 10? T. What is the magnetic energy density for this field? Using the mass-energy relation E = mc², find the mass density that corresponds to the magnetic energy density. Compare this to the mass density of the neutron star, assuming it has the mass of the sun in a sphere of radius 10 km.
(c) Again, assume the magnetic field of the Earth in the region outside the Earth is a pure dipole field corresponding to a dipole moment m = 8 ! 10²² J/T (this is not completely accurate, because the solar wind cuts off the field at a distance of order 10 Earth radii, but it is a good approximation for this exercise). Calculate the total energy of the magnetic field outside the Earth. Compare the result to the rotational kinetic energy of the Earth.

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