Visualizing the Potential of a Spherical Shell

In summary: The potential at any point inside the inner radius is the same as the potential at any other point inside the inner radius. The potential is the same throughout the shell because the field inside the shell is linear.
  • #1
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Homework Statement


The inner radius of a spherical shell is 14.6 cm, and the outer radius is 15.2 cm. The shell carries a charge of 5.35 × 10-8 C, distributed uniformly though its volume.

Sketch, for your own benefit, the graph of the potential for all values of r (the radial distance from the center of the shell).
what would the graph look like? i think it has positive asymptotes at r = +/- 15.2cm (assuming r = 0 is at the origin) but I am not whether it crosses the axis on the interval [-14.6, 14.6] or whether it comes to a minimum
What is the potential at the center of the shell (r=0)?

im not sure how to approach this problem...

-thanks
 
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  • #2
By way of a hint, the problem is nearly identical to Newtonian gravity for a spherically symmetric body of uniform mass density.
 
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  • #3
should the potential be zero due to the equation V = Kq/r ?
 
  • #4
shoe02 said:
should the potential be zero due to the equation V = Kq/r ?

Nope.

You mist know that the potential at any point is the amount of work done in bringing a charge from infinity to that point.

The work done to bring from infinity to outer surface can be found from your formula given above.

In the region bound by the inner and the outer surfaces you will have to find the potential by integrating infinetisally small shells whose radii range from the given inner radii to the outer. As far as the potential at the center it would be same as that as any other point inside the inner radii
 
  • #5
ok thanks. that helps a lot, and i didnt think of potential that way, but it makes a lot more sense now.

thanks again for the help
 
  • #6
well so...why would we be the potential be same for the points inside the inner radii. And how will you integrate? Hint E.dx = dV
 
  • #7
is the equation i integrate this: ((K*q)/r^2)dr
and is it the potential same throughout the shell because the field inside the shell is linear?

again, thanks for the help
 
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1. What is a spherical shell?

A spherical shell is a three-dimensional shape that resembles a hollow sphere. It has a curved surface and is often used to describe objects such as bubbles or planets.

2. How can the potential of a spherical shell be visualized?

The potential of a spherical shell can be visualized by creating a 3D graph that shows the distribution of the potential around the shell. This can be done using mathematical equations and visualization software.

3. What factors affect the potential of a spherical shell?

The potential of a spherical shell is affected by the mass and distribution of the shell, as well as the distance from the center of the shell. Other factors such as external forces or the presence of other objects can also influence the potential.

4. Why is it important to visualize the potential of a spherical shell?

Visualizing the potential of a spherical shell can help scientists understand how gravity or other forces act on objects with a spherical shape. It can also provide insights into the behavior of systems with multiple spherical objects, such as planetary systems.

5. How does visualizing the potential of a spherical shell relate to real-world applications?

Understanding the potential of a spherical shell is crucial in fields such as astronomy and physics, as it helps scientists model and predict the behavior of objects in space. It can also have practical applications in areas such as engineering, where spherical objects are often used in structures and designs.

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