# Electric field from concentric spheres

• tony873004
In summary, for two concentric spherical surfaces with radii R1 and R2 carrying a total charge Q, the electric field between the two shells can be calculated using Gauss' law as \overrightarrow E = \frac{Q}{{4\pi r^2 \varepsilon _0 }}{\rm{\hat r}}, assuming the surface charge density is uniform on each surface. However, if the charge is not uniformly distributed, there is no general formula to describe the field.
tony873004
Gold Member
Two concentric spherical surfaces with radii R1 , R2 each carry a total charge Q. What is the electric field between the two shells?

I don't know what kind of answer they are expecting. Do I just describe it? Here's my attempt:

The field lines from the inner shell will point away from the inner shell towards the outer shell. The field lines from the outer shell will point away from the outer shell towards the inner shell. Since the outer shell has the same total charge as the inner shell, but it is spread out more over the larger surface area, the point where the field lines meet will be closer to the outer shell.

$$\frac{{4\pi r_1^2 }}{{4\pi r_2^2 }} = \frac{{r_1^2 }}{{r_2^2 }}$$
So the field lines from the inner sphere will be $$\frac{{r_1^2 }}{{r_2^2 }}$$
stronger than from the outer sphere. So the distance is $$\frac{{\frac{{r_1^2 }}{{r_2^2 }}}}{{1 + \left( {\frac{{r_1^2 }}{{r_2^2 }}} \right)}}$$ times the distance between the spheres, closer to the outer sphere.

Is this right? Is this even the way I should express the answer?

tony873004 said:
don't know what kind of answer they are expecting. Do I just describe it? Here's my attempt:
The field or the electrical intensity is a mathematical quantity, a vector in fact, and should be written as such.

The field lines from the inner shell will point away from the inner shell towards the outer shell. The field lines from the outer shell will point away from the outer shell towards the inner shell. Since the outer shell has the same total charge as the inner shell, but it is spread out more over the larger surface area, the point where the field lines meet will be closer to the outer shell.
The description is wrong.

Is this right? Is this even the way I should express the answer?
Not right, and no, you should express your answer mathematically. Read up on Gauss' law and fields due to charged shells.

Thanks, Shooting star.

Reading up on it, it seems that there are no field lines inside a shell. So would that mean that the outer shell can simply be ignored? Is the answer simply $$\overrightarrow E = \frac{Q}{{4\pi r^2 \varepsilon _0 }}{\rm{\hat r}}$$ ?

tony873004 said:
Two concentric spherical surfaces with radii R1 , R2 each carry a total charge Q. What is the electric field between the two shells?

This was the original framing of the problem. Here, we have tacitly assumed (and the problem-maker probably implied) that the surface charge density on the shells are uniform. In that case, the expression you have given is correct.

On the other hand, in the problem it is only mentioned that the the total charge is Q on each surface. If it is not uniformly distributed on each surface, then there is no general formula to describe the field.

It wouldn't be the first time this book expected me to assume something. This problem reminds me of the gravity analog. If all Earth's mass were concentrated in a shell with Earth's diameter, gravity would be 1g on the outside surface and 0 everywhere inside.

## 1. What is an electric field from concentric spheres?

An electric field from concentric spheres refers to the electric field that is created between two or more spherical objects with a common center point. This type of electric field is often studied in physics and engineering to understand the behavior of electric charges and how they interact with each other.

## 2. How is the electric field calculated between concentric spheres?

The electric field between concentric spheres is calculated using the inverse square law, which states that the electric field is inversely proportional to the square of the distance between the two objects. This means that the electric field decreases as the distance between the spheres increases.

## 3. Can the electric field be zero between concentric spheres?

Yes, the electric field can be zero between concentric spheres if the charges on the spheres are equal in magnitude and opposite in sign. This would result in a net charge of zero and therefore no electric field between the spheres.

## 4. How does the electric field change with the size of the spheres?

The electric field between concentric spheres is directly proportional to the size of the spheres. This means that as the size of the spheres increases, the electric field also increases. However, the shape and distance between the spheres also play a role in determining the strength of the electric field.

## 5. What are some real-world applications of electric fields from concentric spheres?

Electric fields from concentric spheres have various real-world applications, including in particle accelerators, capacitors, and high voltage power lines. They are also used in medical devices such as MRI machines and in scientific research to study the behavior of electric charges.

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