Potential in case of concentric shells program

In summary, the problem discusses three concentric spherical metallic shells with different charge densities and radii. The potential of these shells can be calculated using the formula ##V = \frac{Q}{4πε_0r}##, where r represents the radius of each shell. The potential of a conductor is uniform throughout the conductor, including on the surfaces and inside the material itself. This is because a conductor conducts charge until there is no more potential difference.
  • #1
gracy
2,486
83

Homework Statement


Three concentric spherical metallic shells A , B and C of radii a , b and c (a<b<c)have charge densities σ,−σandσ respectively . If the shells A and C are at the same potential then the relation between a , b and c is

Homework Equations


##V##=##\frac{Q}{4πε0r}##

The Attempt at a Solution


I know the solution
shells.png


nation.png
[/B]
but I want to know what does it mean potential of shell A or potential of shell B,I mean what value I shall put in place of r in the formula
##V##=##\frac{Q}{4πε0r}## for shell A,B and C?
Does potential of shell A or potential of shell B etc mean potential at the surface of shell A ,B respectively ?
 
Last edited:
Physics news on Phys.org
  • #2
Yes.
You mislead yourself by coloring in the volume of A and the volume between B and C.

There is no formula ##V = \frac{1}{4πε_0r}##; typo :biggrin: ?

But the r in ##V = \frac{Q}{4πε_0r}## is a for A, b for B and c for C :smile: .

And the potential at a position ##\vec r## is the energy per Coulomb it takes to move a test charge from infinity (Where V = 0) to the position ##\vec r##
 
  • Like
Likes gracy
  • #3
BvU said:
Yes.
Were you answering this
gracy said:
Does potential of shell A or potential of shell B etc mean potential at the surface of shell A ,B respectively ?
 
  • #4
Yes
BvU said:
But the r in ##V = \frac{Q}{4πε_0r}## is a for A, b for B and c for C :smile: .
Note that you can't use this for A due to the presence of B and C, nor for B due to the presence of C.
You see that in the solution at the first ##\therefore##

I've always wanted to use that symbol ##\therefore## ! this is the first time :cool:
 
Last edited:
  • Like
Likes gracy
  • #5
gracy said:
Does potential of shell A or potential of shell B etc mean potential at the surface of shell A ,B respectively ?
Yes.

In electrostatics, the potential of a conductor is uniform throughout the conductor.
 
  • Like
Likes gracy
  • #6
SammyS said:
potential of a conductor is uniform throughout the conductor.
Did you mean potential of a conductor is same anywhere inside the conductor as well as on the surface of the conductor?
 
  • #7
gracy said:
Did you mean potential of a conductor is same anywhere inside the conductor as well as on the surface of the conductor?
gracy said:
Did you mean potential of a conductor is same anywhere inside the conductor as well as on the surface of the conductor?
Everywhere in the conducting material itself, as well as on the surfaces.
 
  • #8
Easy to remember: a conductor conducts. If there would be a potential difference, charge would be conducted until there's no more potential difference.
 
  • Like
Likes gracy

FAQ: Potential in case of concentric shells program

What is the "Potential in case of concentric shells program"?

The "Potential in case of concentric shells program" is a scientific program that calculates the electric potential between two concentric spherical shells. It is commonly used in the study of electrostatics and can be applied to a variety of real-world scenarios.

How does the program calculate the electric potential?

The program uses the formula V = kQ/r, where V is the electric potential, k is the Coulomb's constant, Q is the charge on the shell, and r is the distance from the center of the shells. This formula takes into account the inverse relationship between the potential and the distance from the shells.

What are some real-world applications of this program?

The program can be used to calculate the potential between two conductive spheres, such as in the design of capacitors. It can also be applied to the study of biological systems, such as the interaction between charged molecules in cells.

Are there any limitations to this program?

While the program provides accurate results for ideal concentric shells, it may not be applicable in cases where the shells are not perfectly spherical or have uneven charge distributions. It also assumes a vacuum between the shells and does not take into account the effect of other external charges.

How can this program be useful for scientists?

The "Potential in case of concentric shells program" can be a valuable tool for scientists studying electrostatics, as it allows for quick and accurate calculations of the electric potential between two shells. It can also be used as a basis for more complex calculations and simulations in various fields of science and engineering.

Back
Top