Please clearly show the math work on how to get the answers for the questions below

1. [6] Make an estimate of the energy U stored in the Earth's magnetic field Be by finding the energy density in the field at the Earth's surface and multiplying by the volume of the Earth. Typical values of Be are 0.5 Gauss = 50 uT. The radius of the Earth is Re = 6.4 105 km. Earth U 2. [6] During a "solar storm" the Earth's magnetic field is "shaken". The magnetic field may vary by as much as 300 nT/min. Imagine a "Geo- engineering" project where a conducting loop with 1000 km radius is built around the North Pole as indicated in the figure. Find the magnitude of the emf & around the loop during such a solar storm.