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Is there any relation between gravity and electrostatic forces like the formulae for forces of gravity and electrostatics are similiar and the charge plays the same role for electrostatics like mass plays for gravity. Are there also any differences also between them?

Qmechanic
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Abhinav
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  • Possible duplicates: https://physics.stackexchange.com/q/47084/2451 and links therein. – Qmechanic Apr 26 '18 at 03:57
  • I recalled this question in researchgate and someone said the subject was called GEM You might found this interesting https://en.wikipedia.org/wiki/Gravitoelectromagnetism#Equations – J C Apr 26 '18 at 04:01

2 Answers2

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There is no relation between gravity and electrostatic forces in spite of the obvious similarity between Newton's $\frac {1}{r^2}$ force law of gravitation and Coulombs $\frac {1}{r^2}$ law of electrostatic force. A difference: The gravitation law is only attractive, Coulomb's law can be attractive or repulsive, depending on the sign of the charges. In general relativity, electromagnetic fields can contribute to gravity.

freecharly
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I will try to give some important similarities and differences. These lists are in no way exhaustive.

Similarities:

  1. Both the theories rely on a vector field(or its corresponding potential) to describe how other particles with mass/electric charge behave in a region gravitationally or electrically.

    The central quantity of interest in Newtonian gravity is the gravitational field(or gravitational acceleration) or gravitational potential which characterises the amount of gravitational interaction a test particle will have if placed somewhere in the region where there is non-zero gravitational field.

    The central quantity in electrostatics is the electric field or electric potential which influences a test charge whenever it comes into a region of non-zero electric field.

  2. Both the theories obey Gauss' flux law which states that the flux of gravitational field or the electric field through a closed surface is proportional to the total charge(mass/electric charge) enclosed by the surface.

    Mathematically, one writes:

    ${\displaystyle \nabla \cdot \mathbf {g} =-4\pi G\rho ,}$ for gravitational field $\mathbf {g}$ and mass density $\rho$.

    and ${\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{0}}}}$ for electric field $\mathbf {E}$ and charge density $\rho$

  3. Once the field is set up by some source(mass or charge), a test mass or charge interacts with the field via some force.

    For gravitational interaction, it is given by the Newton's law of gravitation: $\mathbf {F}=m_{test} \mathbf{g}$

    For electrostatic interaction, it is given by the Lorentz force law: $\mathbf{F}=q_{test} \mathbf{E}$

    Note that Coulomb's law emerges from Gauss' law and Lorentz force law. Also the identical inverse square dependence on distance arises because of Gauss' law and subsequently the force law.

Differences:

  1. Mass is not quantized whereas charge is.
  2. Mass is of only one type whereas charge comes in two varieties viz. positive and negative. Hence gravitational force is always attractive unlike electrostatic force which can be attractive or repulsive.
  3. Moving electric charge produces both electric and magnetic field, but moving mass doesn't produce any new field.