Simpleton's Thread with Problems

[simpleton]

Hi, here are a list of questions I have doubts about (I do not want to create one for every problem so as not the spam the forum)

Q1.

Homework Statement

My senior gave me this problem.

Given that the Earth's radius at the equator is Re, and the radius at the poles is Rp, express the ratio Re/Rp in terms of known constants.

Homework Equations

I have no idea how to do this problem at all. I don't even know where to start. I asked my senior and he said that over a sufficiently long timescale the rocky material of the Earth can be taken to inelastically deform like a fluid. I don't get that how this information helps :(. Can someone tell me how you even start on these kind of problems?

The Attempt at a Solution

No Attempt.

Q2.

Homework Statement

The problem I am talking about is this:

Given a charged solid sphere with charge density rho and radius R, find the total electrical potential energy in the sphere.

Homework Equations

See below.

The Attempt at a Solution

I found the answer to this problem on this forum.

You start from a small charged sphere of radius r. The amount of charge in it is 4/3*pi*r^3*rho. Then you add a small shell of charge over it, and you find the potential energy. This small shell will have a charge of 4*pi*r^2*dr*rho. Therefore, the potential energy between the sphere and the shell will be:

k*4/3*pi*r^3*rho*4*pi*r^2*dr*rho/r = k*16/3*pi^2*rho^2*r^4^dr

Integrating this from 0 to R, you get k*16/15*pi^2*rho^2*r^5

However, what happens to the potential energy that is within the shell itself? I believe that there should be potential energy between the charges in each shell too, but it does not seem to be taken into account in this solving method.

Q3)

Homework Statement

Find the potential energy of different charged geometric shapes with charge density rho (a line of charges, a sheet of charges, a pyramid, a square etc...)

Homework Equations

U = qV
Gauss Law? integral E dA = Q/Eo

The Attempt at a Solution

I tried doing it for a line in the way the potential energy for the circle is done. I imagine I already have a rod, and I add a tiny bit to the top. However, in the sphere case, I can treat the sphere already there as a point charge, and so I can add the shell of charge easily. However, I don't know how to do so if it is a line, a sheet etc, as there seems to be no symmetry and stuff I can take advantage of.

EDIT: For Q3, I think I just need some guidance, and maybe 1 sample solution to one of the problem. Then I try to work out the rest myself and post my answer here to see whether it is correct. Thanks.

Thanks in advance.

 

[anathema]

Hi there,

I understand your confusion with these problems. Let me try to provide some guidance and explanations to help you understand and solve them.

Q1. In this problem, you need to use the concept of the Earth's shape and its ability to deform like a fluid over time. This is important because it allows us to assume that the Earth is a perfect sphere, with the same radius at all points. This means that Re and Rp can be considered as the same value. From here, you can express the ratio of Re/Rp in terms of the known constant, which is the radius of the Earth (Re). I suggest starting by looking into the formula for the surface area of a sphere and see if you can manipulate it to express Re/Rp.

Q2. In this problem, you have already found the solution, but you are wondering about the potential energy within the shell itself. Remember that potential energy is a measure of the work done to bring a charge from infinity to a certain point in space. In this case, the potential energy between the sphere and the shell is the only one that needs to be considered, as the potential energy within the shell itself is already accounted for in the calculation of the potential energy between the sphere and the shell. Think of it this way - the potential energy within the shell is already taken into account when you calculate the potential energy between the sphere and the shell, as the charges within the shell are interacting with each other as well.

Q3. For this problem, you can use the formula U = qV to calculate the potential energy for different charged geometric shapes. For example, for a line of charges, you can consider each charge as a point charge and use the formula for the potential energy between two point charges. For a sheet of charges, you can use the formula for the potential energy between a point charge and a charged plane. For a pyramid or square, you can use the formula for the potential energy between a point charge and a charged solid sphere, with the appropriate radius. I suggest starting with one shape and trying to solve it using these formulas, and then applying the same concept to the other shapes.

I hope this helps. Good luck with your problem-solving!

 

[tomcue]

I would suggest that you start by breaking down the problem into smaller, more manageable parts. For Q1, it may be helpful to review your knowledge of geometric shapes and how to calculate ratios. You can also research the terms "Earth's radius at the equator" and "Earth's radius at the poles" to gather more information.

For Q2, it is important to understand the concept of potential energy and how it relates to charged objects. It may be helpful to review the equations and try to understand the logic behind them. Additionally, you can try to solve similar problems to gain a better understanding.

For Q3, it may be helpful to start by reviewing the concept of potential energy and how it is calculated for different shapes. Then, you can try to apply the equations and concepts to the specific shapes listed in the problem. It may also be helpful to look for sample solutions or worked examples online to guide your understanding.

Overall, it is important to approach each problem with a clear and logical mindset. Break down the problem into smaller parts, research and review relevant concepts and equations, and seek guidance or worked examples when needed. With persistence and practice, you will be able to successfully solve these problems and gain a deeper understanding of the concepts involved.