Answer:
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 = [tex]8.0\times 10^{- 5}\ T[/tex]
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:
[tex]e = - l(vec{v}\times \vec{B})[/tex]
Here, velocity v is perpendicular to the rod
Thus
e = lvB (1)
For the orbital velocity of the satellite at an altitude, H:
[tex]v = \sqrt{\frac{Gm_{E}}{R_{E}} + H}[/tex]
where
G = Gravitational constant
[tex]m_{e} = 5.972\times 10^{24}\ kg[/tex] = mass of earth
[tex]R_{E} = 6371\ km[/tex] = radius of earth
[tex]v = \sqrt{\frac{6.67\times 10^{- 11}\times 5.972\times 10^{24}}{6371\times 1000 + 400\times 1000} = 7670.018\ m/s[/tex]
Using this value value in eqn (1):
[tex]e = 1.76\times 7670.018\times 8.0\times 10^{- 5} = 1.08\ V[/tex]