How can the electric potential of a dust grain in Saturn's rings be determined?

In summary, the conversation discusses the composition of Saturn's rings, specifically the presence of tiny dust grains in a dilute ionized gas. The question is posed about how many electrons one of these grains would need to pick up in order to have a potential of -400V on its surface, assuming a spherical shape with a radius of 1.0*10^-6m. The conversation also mentions the equations for electric potential and potential energy, but the asker is unsure of how to use them to solve the problem. They also inquire about alternative methods of solving the problem without using the equation in question.
  • #1
Malgrif
18
0

Homework Statement


Much of the material making up Saturn's rings is in the form of tiny dust grains having radii on the order of 10^-6 these grains are located in a region containing a dilute ionized gas, and they pick up excess electrons. As an approximation suppose each grain is sphereical, with radius R=1.0*10^-6m. How many electrons would one grain have to pick up to have a potential of -400V on its surface. (taking V=0 at infinity)?


Homework Equations


V=U/q
V=-W/q


The Attempt at a Solution


not quite sure where to start. I think V=-400=U/q but I don't know how to get U. I'd like to understand why U is relevant in this question also. Thanks
 
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  • #2
What is the electric potential of a conducting sphere of radius r and charge Q ?
 
  • #3
SammyS said:
What is the electric potential of a conducting sphere of radius r and charge Q ?

oh alright. is there another way to solve that problem without relying on that though. That equation is presented in a later section and the question is presented with only knowledge of potential energy and electric potential assumed.
 

1. What is electric potential?

Electric potential is a measure of the potential energy of a charged particle in an electric field. It is defined as the amount of work needed to move a unit positive charge from one point to another in an electric field, without any acceleration.

2. How is electric potential different from electric field?

Electric potential is a scalar quantity, while electric field is a vector quantity. This means that while electric potential only has a magnitude, electric field has both magnitude and direction. Additionally, electric potential is a measure of potential energy, while electric field is a measure of the force experienced by a charged particle.

3. What is the electric potential of dust?

The electric potential of dust refers to the potential energy of charged dust particles in an electric field. This can vary depending on the charge and size of the dust particles, as well as the strength of the electric field they are in.

4. How does dust affect the electric potential in a system?

Dust particles can affect the electric potential in a system by altering the electric field. This is because dust particles can become charged due to friction, and their presence can create areas of higher or lower electric potential. This can also affect the movement and behavior of other charged particles in the system.

5. What are some applications of studying the electric potential of dust?

Studying the electric potential of dust can have various applications, such as understanding the behavior of dust particles in space and the formation of planetary rings. It can also be useful in industries such as semiconductor manufacturing, where controlling the electric potential is crucial for the performance of electronic devices. Additionally, understanding the electric potential of dust can also aid in the development of air pollution control technologies.

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