Visualizing the Potential of a Spherical Shell

[shoe02]

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​

 

[Phrak]

By way of a hint, the problem is nearly identical to Newtonian gravity for a spherically symmetric body of uniform mass density.

 

[shoe02]

should the potential be zero due to the equation V = Kq/r ?

 

[FedEx]

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

 

[shoe02]

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

 

[FedEx]

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

 

[shoe02]

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