Solar Magnetic Energy. Magnetic fields within a sunspot

Chapter 30, Problem 30.47

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Solar Magnetic Energy. Magnetic fields within a sunspot can be as strong as 0.4 T. (By comparison, the earth's magnetic field is about 1/10,000 as strong.) Sunspots can be as large as 25,000 km in radius. The material in a sunspot has a density of about \(3\times10^{-4}\mathrm{\ kg}/\mathrm{m}^3\). Assume \(\mu\) for the sunspot material is \(\mu_{0}\). If 100% of the magnetic-field energy stored in a sunspot could be used to eject the sunspots material away from the sun's surface, at what speed would that material be ejected? Compare to the sun's escape speed, which is about \(6\times10^5\mathrm{\ m}/\mathrm{s}\). (Hint: Calculate the kinetic energy the magnetic field could supply to \(1\mathrm{\ m}^3\) of sunspot material.)