# Electricity and magnetism (Gauss' law)

• Silentwhale
In summary, the problem involves two spherical shells with radii r1 and r2, where the inner shell has a uniformly distributed charge Q1 and the outer shell has a charge Q2. The task is to find the electric field and potential at all points using the given information. The solution involves using Gauss's law and the equation for electric potential, with separate calculations for different domains of radius.
Silentwhale

## Homework Statement

Given two things spherical shells radii r1 and r2 with r2 > r1.
The inner she'll is charged uniformly with a total charge Q1, while the outer shell with Q2.

A) use gauss law to computer the electric field everywhere
B) Use any method to calculate the potential everywhere.

## The Attempt at a Solution

I will be attempting this problem soon just wanted to post the question so I wouldn't waste time it is for my midterm practice. Thank you. I will post my trial solution when I am done trying this problem. Thank you

OK so here is my attempt to the problem:

A) EA = (Qin/ε) (volume ratio)

E (
4(pi)r1^2) = (Q1/ ε) ((4/3 pi r1^3)/(4/3 pi r2^3))

E (
4 pi r1^2) = Q1 r1^3 / ε r2^2

E=
Q1 r1^3 / ε r2^3 4pi r1^2

E
= Q1 r1 / 4pi ε r2^3

E
= KQ1 r1 / r2^3 final answer for a

B)
v= kQ1/r1 + kQ2/r2

V
= (9 x 10^9 Nm^2/ c^2)(Q1/r1 + Q2/r2) answer part b

Silentwhale said:
A) EA = (Qin/ε) (volume ratio)

Volume ratio? You have a typo in your post, but I believe what you intended to type was “thin shell”. Your “volume ratio” suggests you are considering these to be uniform charge densities. Also, even if that were the case, the electric field will have different functional forms over different domains of radius. You have to find a separate answer for each domain.

I do not understand where A) came from. What is this volume ratio? As pointed out in post #3, you are asked to find the electric field everywhere, so first take the case where you want the electric field somewhere inside the inner sphere. Write down the law of physics that you are going to use to solve the problem and aply that law.

## 1. What is Gauss' law?

Gauss' law is a fundamental law of electromagnetism that relates the electric flux through a closed surface to the net electric charge enclosed by that surface.

## 2. How is Gauss' law expressed mathematically?

Gauss' law is expressed as ΦE = qenc0, where ΦE is the electric flux through a closed surface, qenc is the net electric charge enclosed by that surface, and ε0 is the permittivity of free space.

## 3. What is the significance of Gauss' law?

Gauss' law is significant because it allows us to calculate the electric field at a point using the distribution of charges in the surrounding space. It is also used to derive other important laws and equations in electromagnetism.

## 4. Can Gauss' law be applied to magnetic fields?

No, Gauss' law only applies to electric fields. There is a similar law, called Gauss' law for magnetism, which relates the magnetic flux through a closed surface to the net magnetic charge enclosed by that surface.

## 5. What are some real-world applications of Gauss' law?

Gauss' law is used in many practical applications, such as determining the electric field inside a capacitor, calculating the force between two charged objects, and understanding the behavior of lightning strikes. It also plays a crucial role in the design of electronic devices and circuits.

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