# Average electrostatic field over a spherical volume

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• Ahmed1029
In summary, the conversation discusses the formula for the average electrostatic field over a spherical volume of radius R, which is the same expression for the electrostatic field at the position of a point charge in a volume of uniform density with a total charge of (negative)q. However, since the expression blows up at the position of the point charge in both cases, there must be an additional expression involving the dirac delta function for the infinitesimal volume at the point charge's position. It is questioned whether this average field is actually meaningful, especially since it is zero for uniform charge distribution. There is also a curiosity about how to handle the electric field blowing up at the origin in classical theory.
Ahmed1029

this formula in the picture is the average electrostatic field over a spherical volume of radius R. It is the same expression of the electrostatic field, at the (position) of the point charge, of a volume of charge of uniform density whole entire charge is equal to (negative)q.

My question is : since the expression blows up at the position of the point charge in both cases, we know that this integrand isn't the whole story and there is an expression involving the dirac delta function for the infinitesimal volume at the position of the point charge in both cases. How do we conclude then that the average field is the same in both cases? sure they are the same away from the (position) of the point charge, but what guarantees that in an infinitesimal volume where the electric field blows up in both cases they are going to be the same? Maybe the expression involving the delta function is different in either case!

Also I'm curious to know if the electric field blowing up at the origin is just a shortcoming of the classical theory. If so, how do I deal with it in my calculations?

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Ahmed1029 said:
It is the same expression of the electrostatic field, at the (position) of the point charge, of a volume of charge of uniform density whole entire charge is equal to (negative)q.
This is impossible to parse. What is your charge distribution and what are you trying to compute?

This average is meaningless. For uniform charge distribution it is zero anyway. The field is a vector and for any given elementary volume there is another one with the vector in the opposite direction.

Ahmed1029

## 1. What is the definition of "Average Electrostatic Field over a Spherical Volume"?

The average electrostatic field over a spherical volume is the measure of the strength and direction of the electric field within a sphere, calculated by taking the sum of the electric field at each point within the sphere and dividing it by the total volume of the sphere.

## 2. How is the average electrostatic field over a spherical volume calculated?

The average electrostatic field over a spherical volume is calculated by taking the integral of the electric field over the entire spherical volume and dividing it by the total volume of the sphere.

## 3. What factors can affect the average electrostatic field over a spherical volume?

The average electrostatic field over a spherical volume can be affected by the charge distribution within the sphere, the distance from the center of the sphere, and the dielectric constant of the material surrounding the sphere.

## 4. How is the average electrostatic field over a spherical volume different from the electric field at a single point?

The average electrostatic field over a spherical volume takes into account the electric field at all points within the sphere, while the electric field at a single point only measures the strength and direction of the electric field at that specific point.

## 5. Why is the average electrostatic field over a spherical volume important in scientific research?

The average electrostatic field over a spherical volume is important in scientific research because it allows scientists to accurately measure and understand the electric field within a spherical volume, which is useful in a variety of fields such as physics, chemistry, and engineering.

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