# Field between 2 conducting spheres in electric field

• oliverroth

#### oliverroth

Hi,
I tried to make some simulations of two conducting spheres in a constant electric field. The simulations seem to indicate that the electric field in the gap increases with increasing diameter of the spheres at a constant gap distance. Does this make sense? I expected just the reverse. What is wrong? Does an analytical solution for this problem exist?
I really appreciate any help.

If I approximate the added field at the center of the gap as due to two induced dipoles,
I get $$E=\frac{4E_0}{(1+d/2R)^3}$$. This agrees with what you found.

Thanx a lot. This matches qualitatively (although it still sounds odd to me). Can you tell me how you have derived this result?

A conducting sphere in constant electric field E_0 gets an induced dipole moment
$$p=E_0 R^3.$$. The electric field a distance R+d/2 from a dipole is
$$E=2p/(R+d/2)^3.$$ Put these together to get the answer.

Ok. Thank you.

## 1. What is the purpose of studying the field between 2 conducting spheres in an electric field?

The purpose of studying this topic is to understand the behavior of electric fields and how they interact with conductors. This knowledge is essential in various fields such as electrical engineering, physics, and materials science.

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

The electric field between 2 conducting spheres can be calculated using the formula E = Q/(4πεr^2), where E is the electric field, Q is the charge on each sphere, ε is the permittivity of free space, and r is the distance between the spheres.

## 3. What is the significance of the distance between the conducting spheres?

The distance between the conducting spheres affects the strength of the electric field between them. As the distance increases, the electric field decreases, and vice versa. This relationship is described by the inverse square law.

## 4. How does the presence of a dielectric material between the conducting spheres affect the electric field?

The presence of a dielectric material, such as air or plastic, between the conducting spheres can decrease the electric field strength. This is because dielectric materials have a higher permittivity than air, which reduces the effective distance between the spheres in the calculation of the electric field.

## 5. What are some real-world applications of the field between 2 conducting spheres in an electric field?

Some real-world applications include capacitors, which use conducting plates separated by a dielectric material to store electric charge, and lightning rods, which use the principle of the electric field between conducting objects to protect buildings from lightning strikes.