# Electric field in a spherical shell

• curiosissimo
In summary, the conversation discusses the Gaussian theorem and how it relates to calculating the electric field. It is mentioned that Q's value is known and does not need to be expressed, and that the surface can be expressed as S=4pi*x^2. However, the resulting equation for E is found to be incorrect, and it is advised not to confuse the total charge of the shell with the charge enclosed by the Gaussian surface.
curiosissimo
Homework Statement
We have a spherical shell with 2 radiuses $$R_1<R_2$$ The charge Q is distributed uniformly in the part of the sphere between R1 and R2. The inner space of the sphere ($$0<y<R_1$$) has no charge What is the electric field in the spherical shell?
Relevant Equations
Gaussian theorem
So for the Gaussian theorem we know that $$\frac{Q}{e} = \vec E \cdot \vec S$$ Q's value is known so we don't need to express it as $$Q=(4/3)\pi*(R_2 ^3-R_1 ^3)*d$$ where d is the density of the charge in the volume. I've expressed the surface $$S=4\pi*x^2$$ where x is the distance of a point in the shell from the center of the sphere. So we simply get $$E=\frac{Q}{e*4\pi*x^2}$$ but it's wrong and I really don't know why. Thanks in advance!

Hello, curiosissimo. Welcome to PF.

Don't confuse the total charge of the shell with the charge enclosed by the Gaussian surface.

curiosissimo
TSny said:
Hello, curiosissimo. Welcome to PF.

Don't confuse the total charge of the shell with the charge enclosed by the Gaussian surface.
Of course! What a silly mistake! Thank you very much!

berkeman

## 1. What is an electric field in a spherical shell?

An electric field in a spherical shell is a type of electric field that exists inside a hollow spherical shell made of a conducting material. It is created by the distribution of electric charges on the surface of the shell.

## 2. How is the electric field calculated in a spherical shell?

The electric field in a spherical shell can be calculated using the formula E = Q/(4πε₀r²), where Q is the total charge on the shell, ε₀ is the permittivity of free space, and r is the distance from the center of the shell.

## 3. Does the electric field inside a spherical shell depend on the distance from the center?

No, the electric field inside a spherical shell is independent of the distance from the center. This is because the electric field inside a conductor is always zero, and the charges on the surface of the shell create a cancellation of the electric field inside.

## 4. What is the direction of the electric field inside a spherical shell?

The direction of the electric field inside a spherical shell is always radial, pointing towards or away from the center of the shell depending on the distribution of charges on the surface.

## 5. Can the electric field inside a spherical shell be non-uniform?

No, the electric field inside a spherical shell is always uniform, meaning it has the same magnitude and direction at all points inside the shell. This is because the charges on the surface of the shell are evenly distributed, leading to a uniform cancellation of the electric field inside.

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