Magnetic fields within a sunspot can be as strong as 0.4T. (By comparison, the e

Question

Magnetic fields within a sunspot can be as strong as 0.4T. (By comparison, the earth's magnetic field is about 1/10,000 as strong.) Large sunspots can be as much as 25,000km in radius. The material in a sunspot has a density of about 3×10^4 kg/m^3.

(a)If 100% of the magnetic field energy stored in a sunspot could be used to eject the sunspot's material away from the sun's surface, at what speed would that material be ejected? (Hint: Calcualte the kinetic energy the magnetic field could supply to 1m3 of sunspot material.)

The answer is v = 2×104 m/s . Could you explain why the answer is v = 2×104 m/s

Explanation / Answer

magnetic field energy density is u = B^2/(2*mu_o) =

energy in 1 m^3 volume is U = B^2/(2*mu_o) =

given that B^2/(2*mu_o) = 0.5*m*v^2

v = B/sqrt(mu_o*m) =

m is the mass of the sunsopt material in 1m^3= 3*10^-4 kg

then v = 0.4/sqrt(4*pi*10^-7*3*10^-4) = 2.0*10^4 m/s

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