Question

The earth has a net negative charge of about -4.3 x 105 C. Since this charge is distributed more or less uniformly over the spherical earth, the force due to this charge is the same as if it were all placed at the Earth's center. A 6.0 kg satellite is orbiting with an orbital radius of 55000 km. If the satellite were also charged, then there would be an electric force in addition to the gravitational force a. What charge (including the sign) would need to be on the satellite to completely cancel the earth's gravitational force on it? b. With this same charge and these same assumptions, what would be the net force on the satellite if instead of being in space it were near the surface of the earth? Hint: Note that the gravitational force is not just mg, you must use Newton's law of gravity since the satellite in part a is not near the earth's surface. For part b, you need not do an extensive calculation. The two kinds of force have very similar formulas. Look carefully at their formulas and think about how they vary with distance.

Answer 1

Given is:-

charge on the Earth

mass of the satellite  

radius  

mass of the Earth  

Now,

Part-a

Since the gravitational force is of attractive type therefore the charge on the satellite must be of negative type so that it can counter gravitational force

so

by plugging all the values we get

which gives us

Part-b

The gravitational force near the Earth's surface is

and the eletrostatic force will be

where R is the radius of the Earth

KQ

by plugging all the values we get

which gives us

Thus the net force on to the sattelite is