Question 7, chap 29, sect 1. part 1 of 2 10 points Assume the Earth\'s magnetic

Question

Question 7, chap 29, sect 1. part 1 of 2 10 points Assume the Earth's magnetic dipole mo- ment is aligned with the Earth's rotational axis, and the Earth's magnetic field is cylin drically symmetric (like an ideal bar mag- netic). The mass of a proton is 1.67262 x 10 kg and the radius of Earth is 6.37 x 106 m. What speed would a proton need to orbit in an exact circle around the Earth at a height of 970 km, where the Earth's magnetic field has an intensity of 4.03 x 10 T? Answer in units of m/s.

Explanation / Answer

q v B = m v^2 / r

v = q r B / m

= (1.602 x 10^-19) (6371 x 10^3 + 970 x 10^3) (4.03 x 10^-8) / (1.673 x 10^-27)

v = 2.83 x 10^7 m/s

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F = I L B

F = 78 x 0.18 x 0.87 = 12.2 N

W = F d = 8.80 J

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