Asatellite, orbiting the earth at the equator at an altitude of 400 km, has an antenna that can be modeled as a 1.76-m-long rod. the antenna is oriented perpendicular to the earth's surface. at the equator the earth's magnetic field is essentially horizontal and has a value of 8.0×10−5t; ignore any changes in b with altitude.
assuming the orbit is circular, determine the induced emf between the tips of the antenna.

The inducerd emf is 1.08 V

Solution:

As per the question:

Altitude of the satellite, H = 400 km

Length of the antenna, l = 1.76 m

Magnetic field, B =

Now,

When a conducting rod moves in a uniform magnetic field linearly with velocity, v, then the potential difference due to its motion is given by:

Here, velocity v is perpendicular to the rod

Thus

e = lvB           (1)

For the orbital velocity of the satellite at an altitude, H:

where

G = Gravitational constant

= mass of earth

= radius of earth

Using this value value in eqn (1):