Total potential energy due to gravitational and electrostatic potential energy

AI Thread Summary
The discussion revolves around calculating the total potential energy of two dust particles, each with the same mass and charge, separated by 0.01 meters. The electrostatic potential energy (E_el) is calculated as 1.128 x 10^-24 J, while the gravitational potential energy (E_grav) is -1.128 x 10^-24 J. There is confusion regarding whether to sum these energies directly or to consider their magnitudes. The conclusion drawn is that the total potential energy should be the sum of E_el and E_grav, leading to a total of zero, which raises questions about the validity of this result. The discussion emphasizes the need to clarify how potential energies are combined in this context.
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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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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?
 
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
 
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