The similarity of form of Newton\'s law of gravitation and Coulomb\'s law caused

Question

The similarity of form of Newton's law of gravitation and Coulomb's law caused some to speculate that the force of gravity is related to the electrostatic force. Suppose that gravitation is entirely electrical in nature--that an excess charge Q on the Moon and an equal and opposite excess charge -Q on the Earth are responsible for the gravitational force that causes the observed orbital motion of the Moon about the Earth. What is the required size of Q to reproduce the observed magnitude of the gravitational force?

Explanation / Answer

gravitational force F = G Mm/r^2....(1)

electrostatic force F = k q1q2/r^2

here in second equation q1 and q2 are same in magnitude but opposite in sign

hence F = kq^2/r^2....(2)

now equating equation 1 and 2 then

q = sqrt(GMm/K)......(3)

where G is the universal gravitational constant = 6.67*10^-11 Nm^2/Kg^2

M is the mass of the earth = 6*10^24 kg

m isthe mass of the moon = 7.4*10^22 kg

k is the permittivity of free space = 9*10^9

substitute all the above values in equation 3 then

q = sqrt[(6.67*10^-11)(6*10^24)(7.4*10^22)/ 9*10^9]

   = 5.7*10^13 C

  

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