# Electrostatic and gravitational forces? [closed]

Electrostatic force between two charged particles depends on the magnitude of the charges and the distance between them. If the charges have mass $m$ and $m'$ then, what will be the total force including gravitational and electrostatics forces? Distance between them is $d$.

• You just calculate the electrostatic and gravitational forces separately then add them together. – John Rennie Apr 5 '14 at 8:36
• But if mass m consists of n number of charges and mass m consists of nm' number of charges.I need a single equation,can u help me sir please? – dipendra Apr 5 '14 at 8:54
• I am new to this site.so,i dont know rules.Sorry for that,i am learning. – dipendra Apr 5 '14 at 17:31

Seeing your comment, it seems you are concerned about group of charges with certain mass. Then you need to apply Gauss law for the cases where it becomes difficult to apply coulombs law or principle of superposition. In case of gravitational force, find the center of masses of either configuration and you can proceed to find force using Newtons law of gravitation. Vector sum of either force will then give your net force.

For sum special cases like force between earth and other planets which also have magnetism, you can add magnetic force for the net force.

The magnitude of gravitational force between them would be: $$G\frac{mm'}{d^2}$$

The magnitude of electrostatic force, if the magnitude of charge on them is $q$ and $q'$ respectively, would be: $$\frac{1}{4\pi \epsilon _o}\frac{qq'}{d^2}$$

The net force would just be the vector sum of the two.

Since $k_e$ is of the order $10^{9}$ and $G$ is of the order $10^{-11}$ thus gravitational force can be neglected, even if you add then can be added safely thus

$F_T = F_g + F_e = G\times\frac{m_1\times m_2}{d^2} + k_e\times\frac{q_1\times q_2}{d^{2}}$