# Total potential energy due to gravitational and electrostatic potential energy

## Homework Statement

Two dust particles are separated by 0.01m and of the same mass and charge, find the total potential energy

## Homework Equations

$$E_{el}=k\frac{q_1 q_2}{r}$$

$$E_{grav}=-G\frac{m_1 m_2}{r}$$

$$r=0.01 m$$, $$q_1=q_2=1.1201\times10^{-18} C$$ $$m_1=m_2=13\times10^{-9} kg$$
Where G and k are the gravitational and Coulomb's constant respectively.

## The Attempt at a Solution

$$E_{el}=1.128\times10^{-24} J$$

$$E_{grav}=-1.128\times10^{-24} J$$

Not sure whether it $$E_{tot}=E_{el}+E_{grav}$$ or $$E_{tot}=\left|E_{el}\right|+\left|E_{grav}\right|$$?

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supratim1
Gold Member
you have found the electric and gravitational field. now calculate the potentials. total will be the sum of the potentials, not sum of their magnitudes.

So the potential energy of the system is zero?

supratim1
Gold Member
why should it be zero?

Well I have found the electrostatic and gravitational potential energies

$$E_{el}=1.128\times10^{-24} J$$
and
$$E_{grav}=-1.128\times10^{-24} J$$

Is it not their sum? I'm taking $$r=0$$ as the particles being together and $$E_{pot}=0$$ at $$r=\infty$$