Total potential energy due to gravitational and electrostatic potential energy

In summary, the conversation discusses finding the total potential energy between two dust particles with the same mass and charge, separated by 0.01m. The equations used are for the electric and gravitational fields, and the values for the constants and particles are given. The solution involves calculating the potentials and adding them together. The question of whether the total energy is zero is raised, but it is clarified that the potential energy at infinity is not necessarily zero.
  • #1
bobred
173
0

Homework Statement


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

Homework Equations


[tex]E_{el}=k\frac{q_1 q_2}{r}[/tex]

[tex]E_{grav}=-G\frac{m_1 m_2}{r}[/tex]

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

The Attempt at a Solution



[tex]E_{el}=1.128\times10^{-24} J[/tex]

[tex]E_{grav}=-1.128\times10^{-24} J[/tex]

Not sure whether it [tex]E_{tot}=E_{el}+E_{grav}[/tex] or [tex]E_{tot}=\left|E_{el}\right|+\left|E_{grav}\right|[/tex]?
 
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  • #2
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
So the potential energy of the system is zero?
 
  • #4
why should it be zero?
 
  • #5
Well I have found the electrostatic and gravitational potential energies

[tex]E_{el}=1.128\times10^{-24} J[/tex]
and
[tex]E_{grav}=-1.128\times10^{-24} J[/tex]

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

1. What is total potential energy?

Total potential energy is the sum of gravitational potential energy and electrostatic potential energy in a system. It represents the amount of energy that an object possesses due to its position or arrangement in a gravitational or electric field.

2. How is gravitational potential energy calculated?

Gravitational potential energy is calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object relative to a reference point. This formula assumes a constant gravitational field.

3. What is electrostatic potential energy?

Electrostatic potential energy is the energy stored in an object due to its electric charge and its position in an electric field. It is calculated using the formula PE = kqQ/r, where k is the Coulomb's constant, q and Q are the charges of the objects, and r is the distance between them.

4. Can total potential energy be negative?

Yes, total potential energy can be negative. This usually occurs when there is a decrease in height or distance in a gravitational or electric field, resulting in a decrease in potential energy. However, the negative sign does not affect the magnitude of the energy.

5. How does the total potential energy change in a system?

The total potential energy in a system can change when there is a change in the position or arrangement of objects in a gravitational or electric field. It can also change when there is a change in the strength or direction of the fields. Generally, potential energy decreases as objects move closer together and increases as they move farther apart.

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