A space shuttle orbits around the earth on the equatorial plane, at a distance R

Question

A space shuttle orbits around the earth on the equatorial plane, at a distance R = 8059 km from the centre of the earth, with a velocity v = 7km/s. A small satellite, orbiting on the equatorial plane as well, is tied to the shuttle by means of a conducting wire of length L = 200m (see figure below). Determine the potential difference delta V between the space shuttle and the satellite, given that the magnetic field of the earth is that of a magnetic dipole located at the centre of the earth and orthogonal to the equatorial plane, and the magnetic field of the earth at the equator has a magnitude B_0 = 5 times 10^-5 T.

Explanation / Answer

The electrical potential energy V between space shuttle and the satellite will be 0,as no current is induced in the metal of the shuttle or the satellite by the magnetic field of the Earth.There is no change in the magnetic flux in the equatorial path ,so no current is induced in the metal of the shuttle or satellite, and even if the path of travel would have been any other path than the equatorial,the potential difference between the space shuttle and the satellite would still be 0,as they are connected with a conducting wire.

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