Please help How to find the potential difference of a spherical shell

In summary, the conversation revolves around finding the electric potential V as a function of distance from the center of a spherical shell of charge Q and uniform volume charge density p. The solution in region a) is V = kQ/r, while in region b) the individual is confused and unsure of how to proceed. In region c), the individual admits they are not able to understand the problem, and in region d), it is mentioned that the answers should agree and if not, a mistake has been made. The conversation also brings up the concept of the electric field being zero inside the shell and using Gauss' Law to determine the behavior of the electric field.
  • #1
stunner5000pt
1,461
2
I can frankly say I'm totally confused on how to solve this problem. Here it is:

A think spherical shell of charge Q and uniform volume charge density p is bounded by radii r1 and r1 where r2>r1. WIth V=0 at infinity find the electric potential V as a function of the distance from the centre of the distribution considering the regions:

a) r > r2 Ans. V = kQ/r because the spherical distribution will act like a point charge when any point is taken outside the shell, by Gauss Law

b) r2 > r > r1 Ans. completely confused here...Using the concept in the first part a) i would think from the iner radii point of view

Vsmall = kQ/r

but since it is enclosed in a bigger radii i have no idea how to proceed

c) r < r1 if the previous confused me then this one is so above my head it's orbiting the earth

d) do these results agree at r = r2 and r = r1 ... Well if i could answer b and c then i might be able to answer this one
 
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  • #2
c) should be easy, if the Electric field is zero inside the shell, what does this say about the potential?

b) is a little trickier. How does the Electric field behave inside the shell? Does it go up as r^2? Use Gauss' Law if you must.

d) The answers should agree, if not, then a mistake has been made.

Claude.
 
  • #3


First of all, don't worry if you are confused about this problem. It can be a bit tricky to understand at first, but with some practice and understanding of the concepts, you will be able to solve it.

To find the potential difference of a spherical shell, we need to use the formula V = kQ/r, where k is the Coulomb's constant, Q is the total charge of the shell, and r is the distance from the center of the shell.

a) In this case, r > r2, which means that the point is outside the shell. As you correctly mentioned, the spherical distribution will act like a point charge and the potential difference can be calculated using the formula V = kQ/r.

b) In this region, r2 > r > r1, we need to take into account the fact that the point is now inside the shell. We can still use the same formula, but we need to consider the charge enclosed within the smaller radius r. This can be done by using Gauss's Law, which states that the electric flux through a closed surface is equal to the charge enclosed by that surface. So, in this case, the potential difference can be calculated as V = kQenc/r, where Qenc is the charge enclosed within the smaller radius r. This can be calculated by subtracting the charge within r1 from the total charge Q.

c) In this region, r < r1, the point is now inside the shell and we need to take into account the charge enclosed within the smaller radius r. The potential difference can be calculated using the same formula as in part b) but with the charge enclosed within r.

d) Yes, the results should agree at r = r2 and r = r1. At these points, the potential difference should be the same since the point is either on the surface or inside the shell.

I hope this helps to clarify the concept. Remember, practice makes perfect, so keep practicing and don't hesitate to ask for help if you are still confused.
 

1. What is a spherical shell?

A spherical shell is a three-dimensional shape that is formed by a thin, hollow sphere. It can be thought of as a hollow ball with no thickness or volume.

2. Why is it important to find the potential difference of a spherical shell?

Finding the potential difference of a spherical shell is important in understanding the electric potential and electric field distribution around the shell. This information is crucial in various applications such as in designing electrical devices or understanding the behavior of charged particles.

3. How do you calculate the potential difference of a spherical shell?

The potential difference of a spherical shell can be calculated using the equation V = kQ/r, where k is the Coulomb's constant, Q is the charge of the shell, and r is the distance from the shell's center. This equation assumes that the shell is a point charge and the distance r is much larger than the radius of the shell.

4. What factors can affect the potential difference of a spherical shell?

The potential difference of a spherical shell can be affected by the charge of the shell, the distance from the shell's center, and the presence of any other nearby charges. It can also be affected by the material of the shell, as well as the external electric field.

5. Are there any other methods to find the potential difference of a spherical shell?

Yes, there are other methods to find the potential difference of a spherical shell, such as using Gauss's law or using the method of images. These methods may be more complex and require a deeper understanding of electromagnetism, but they can provide more accurate results in certain scenarios.

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