Conservation of energy between two charged sheres

In summary, the conversation discusses the conservation of energy between two charged spheres, specifically in relation to their final velocities when they are conducting. The concept of electric potential energy is also mentioned, with the question of how to express the change in energy when the spheres are in electrostatic equilibrium. The instructor clarifies that when the spheres are conducting, the charges migrate and increase the electric field, resulting in a higher final velocity. A simple equation is not required, but rather reasoning.
  • #1
Will
conservation of energy between two charged spheres

We are given two insulating spheres with charges q1 and -q2 separated by a distance d. Using concepts of conservation of energy and linear momentum, I solved for the velocity of each sphere at the point of contact.
We are then asked if the spheres were conducting, would the final velocity be greater. delta-U for the insulating spheres is U-final minus U- initial = Keq1q2(1/(r1+r2) - 1/d)) meaning there is some electric potential energy remaing, because the center of spheres are still separated.
But when the two conducting spheres touch, they are in electrostatic equilibrium, right? So there is no more potential energy, correct? How do I write an expression for the delta-U in this case? I should get a greater value, right?
 
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  • #2
In that case, U-final would be 0 wouldn't it?
 
  • #3
Talked to my instructor today. He said that when the spheres are conducting, the charges migrate across the surface increasing the magnitude of E in between, hence higher V-final. He also said its not a simple equation anymore, but we weren't really asked for one, just to reason that out.
 

1. How does the conservation of energy apply to two charged spheres?

The conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. In the case of two charged spheres, the total energy of the system remains constant as the spheres interact with each other.

2. What is the relationship between the electric potential energy and kinetic energy of the two spheres?

The electric potential energy of the two spheres is converted into kinetic energy as they move closer together due to the attraction between opposite charges. This conversion follows the law of conservation of energy, where the total energy of the system remains constant.

3. Does the distance between the two spheres affect the conservation of energy?

Yes, the distance between the two spheres plays a crucial role in the conservation of energy. As the spheres move closer together, the electric potential energy decreases, and the kinetic energy increases. However, if the distance between the spheres increases, the opposite occurs, and the kinetic energy decreases while the electric potential energy increases.

4. How does the charge of the two spheres affect the conservation of energy?

The charge of the spheres also affects the conservation of energy. If the spheres have opposite charges, they will attract each other, and their electric potential energy will decrease as they move closer together. However, if the two spheres have the same charge, they will repel each other, and their electric potential energy will increase as they move further apart.

5. Is the conservation of energy between two charged spheres affected by external factors?

No, the conservation of energy between two charged spheres is not affected by external factors. As long as the two spheres are isolated from any other external forces, their total energy will remain constant as they interact with each other based on their charges and distances.

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