# Calculating size of charge distribution with a known electric field

• nsatya
In summary, the conversation discusses finding an order of magnitude estimate for the size of a complicated charge distribution, given the electric field it produces. One approach suggested is using Gauss' Law to calculate the total charge enclosed by a spherical surface, with the total charge being known to be 10 times the charge of a proton. This can then be used to determine the minimum radius of the charge distribution.
nsatya

## Homework Statement

A complicated distribution of 10 protron produces a radially symmetric electric field given by,

E(r) = (10*charge_of_proton/4pi*epsilon_0)*(1/r^2 + 100/r^4)*r_hat

Give an order of magnitude estimate for the size of the charge distribution.

## The Attempt at a Solution

I thought that r could be expressed as sqrt(a^2 + z^2), "z" being the distance from the charges, and "a" being the size of the radius of the charge distribution. With this method, I'm having trouble finding the right values for "z" and E(r) that will help me calculate "a". Basically, we know what the electric field looks like, so we should be able to give a rough estimate on the size of the charge distribution. Could anyone point me in the right direction? Any help would be appreciated.

You might try using Gauss' Law to calculate the total charge enclosed by a concentric spherical gaussian surface of radius $r$. You know that the total charge of the distribution is 10 times the charge of the proton, so you can then calculate the minimum radius $r$ for which your Gaussian encloses that amount of charge.

## 1. How do you calculate the size of a charge distribution with a known electric field?

To calculate the size of a charge distribution with a known electric field, you can use the equation Q = ε0 * E * A, where Q is the total charge, ε0 is the permittivity of free space, E is the electric field strength, and A is the area of the charge distribution. This equation assumes that the electric field is uniform and that the charge distribution is a flat surface.

## 2. What is the unit of measurement for the size of a charge distribution?

The size of a charge distribution is typically measured in coulombs (C). This is the standard unit for electric charge and represents the amount of charge that passes through a point in one second when there is a constant current of 1 ampere.

## 3. Can you calculate the size of a charge distribution if the electric field is not uniform?

Yes, you can still calculate the size of a charge distribution with a known electric field if it is not uniform. However, the equation used will be different and will depend on the specific shape and distribution of the electric field. It may also require more complex mathematical calculations.

## 4. How does the size of a charge distribution affect the strength of the electric field?

The size of a charge distribution directly affects the strength of the electric field. As the size of the charge distribution increases, the strength of the electric field decreases. This is because the same amount of charge is spread out over a larger area, resulting in a weaker electric field.

## 5. Can you use the equation for calculating the size of a charge distribution with a known electric field for 3-dimensional charge distributions?

No, the equation Q = ε0 * E * A can only be used for 2-dimensional charge distributions. For 3-dimensional charge distributions, the equation becomes Q = ε0 * E * V, where V is the volume of the charge distribution. This equation is more complex and requires more precise measurements of the electric field and volume of the distribution.

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