Total potential energy due to gravitational and electrostatic potential energy

1. Feb 10, 2011

bobred

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. Feb 10, 2011

supratim1

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. Feb 16, 2011

bobred

So the potential energy of the system is zero?

4. Feb 17, 2011

supratim1

why should it be zero?

5. Feb 17, 2011

bobred

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 $$r=\infty$$