where µis the Earth’s dipole moment and λmis the magnetic latitude. The ratio of the field magnitudes for two different distances at the same latitude is BBrr211323=. With B1being the value at the surface and B2being half of B1, we set r1equal to the radius Reof the Earth and r2equal to Re+ h, where his altitude at which Bis half its value at the surface. Thus, 1233=+RRheebg.Taking the cube root of both sides and solving for h, we get ()( )( )1332121 6370km1.66 10 km.ehR=−=−=×(b) We use the expression for Bobtained in Problem 32-55, part (a). For maximum B, we set sin λm= 1.00. Also, r= 6370 km – 2900 km = 3470 km. Thus, ( ) ( )7222220max3364410T m A8.00 10 A msin131.0044m3.83 10 T.mBrµµ−−π×⋅×⋅=+λ=+ππ3.47×10(c) The angle between the magnetic axis and the rotational axis of the Earth is 11.5°, so λm= 90.0° – 11.5° = 78.5° at Earth’s geographic north pole. Also r = Re= 6370 km. Thus,
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