# Is the charge distribution for an electric field unique?

• Ganesh Ujwal
In summary, the uniqueness theorem in electrostatics states that for a given charge distribution and boundary conditions, there exists only one solution to Poisson's equation and the electric field in that volume is uniquely determined. This means that if we know the electric field and boundary conditions in a region of space, there is only one possible charge distribution that could have produced it. An example of this is that a charge distributed on a sphere will produce the same electric field regardless of the size of the sphere.

#### Ganesh Ujwal

If the electric field and boundary conditions are known exactly for a region of space, is it true that there exists only one charge distribution in that region of space that could have produced it?

My understanding of the uniqueness theorem in electrostatics is that for a given charge distribution and boundary conditions for a volume, there exists only one (unique) solution to Poisson's equation, and thus the electric field in that volume is uniquely determined. Does the arrow point the other way, too? If we know the field and boundary conditions, is the charge distribution uniquely determined in the volume? Is there a simple example that illustrates why or why not?

Charge distributed on a sphere should produce the same electric field regardless of the size of the sphere. For example, if you measure the electric field at a point 1 m from X you can't tell if the the field you observe results from a sphere of 1 cm or 99 cm radius centered at X.

## 1. What is a charge distribution for an electric field?

A charge distribution for an electric field refers to the arrangement of positive and negative charges in a given space. This distribution determines the strength and direction of the electric field in that space.

## 2. How is the charge distribution for an electric field determined?

The charge distribution for an electric field is determined by the distribution of charges in the space. This can be calculated using Gauss's law, which relates the electric field to the enclosed charge within a given surface.

## 3. Is the charge distribution for an electric field unique?

Yes, the charge distribution for an electric field is unique for a given space. This means that the arrangement of charges that create a specific electric field cannot be replicated in another space.

## 4. Can the charge distribution for an electric field change over time?

Yes, the charge distribution for an electric field can change over time. This can happen if the charges within the space are moving or if new charges are introduced into the space.

## 5. How does the charge distribution affect the electric field strength?

The charge distribution directly affects the strength of the electric field. The closer the charges are to each other, the stronger the electric field will be. Similarly, if the charges are spread out, the electric field will be weaker.