# Total potential energy due to gravitational and electrostatic potential energy

1. ### bobred

163
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 $$E_{tot}=\left|E_{el}\right|+\left|E_{grav}\right|$$?

2. ### supratim1

280
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.

3. ### bobred

163
So the potential energy of the system is zero?

4. ### supratim1

280
why should it be zero?

5. ### bobred

163
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 $$r=\infty$$