## Total potential energy due to gravitational and electrostatic potential energy

1. The problem statement, all variables and given/known data
Two dust particles are separated by 0.01m and of the same mass and charge, find the total potential energy

2. Relevant 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.

3. 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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 Recognitions: 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?

Recognitions:
Gold Member

## Total potential energy due to gravitational and electrostatic potential energy

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 $$r=\infty$$