# How does the size of an atom affect its electric field energy?

• jmb741
In summary, the conversation discusses finding the total electric field energy for a hydrogen atom and its electron and proton, taking into consideration the charge distribution and the separation of charges. It also mentions some helpful resources for further understanding.
jmb741

1a) The hydrogen atom has a single electron in a fixed orbit around the proton with a radius of (5.29 E-11 m). Find the total electric field energy U(E) for the electron and proton assumming that each one has a radius of (1.00E-15 m).

1b) Included the additional contribution to the electrical potential energy U'(E) if we consider the charge within the proton as a uniform charge distribution.

Electric field energy density is

$$u=e_0E^2/2$$

The numbers give you the separation of the charges, and I assume the radii are to be used to treat the charge as distributed over the surface in part a) and then uniformly distributed for the proton in part b)

http://www.phys.ufl.edu/~rfield/classes/spring01/images/chp31_3.pdf
http://www.phys.ufl.edu/~rfield/classes/spring01/images/chp31_4.pdf
http://www.physics.gla.ac.uk/~dland/ELMAG305/Elmag305txt3.pdf

Last edited by a moderator:

The size of an atom does not directly affect its electric field energy. The electric field energy of an atom is determined by the distribution of charge within the atom and the distance between the charges. However, the size of an atom can indirectly affect its electric field energy by influencing the distribution of charge within the atom.

In the case of the hydrogen atom described in the problem, the size of the atom is given by the radius of the electron's orbit and the radius of the proton. These values are used to calculate the total electric field energy (U(E)) of the atom, which is the sum of the electric potential energies of the electron and the proton.

However, if we consider the charge within the proton as a uniform distribution, this will add an additional contribution to the electric field energy (U'(E)). This is because the uniform distribution of charge will create a more complex electric field, resulting in a higher electric field energy.

To solve the problem, the given values of the radius of the electron's orbit and the proton can be used to calculate the electric field energy (U(E)) using the formula U(E) = kq1q2/r, where k is the Coulomb's constant, q1 and q2 are the charges of the electron and proton respectively, and r is the distance between them.

For part 1b, the additional contribution to the electric field energy (U'(E)) can be calculated by considering the uniform charge distribution within the proton. This can be done using the formula U'(E) = (3/5)kq1q2/r, where the factor (3/5) takes into account the distribution of charge within the proton.

In conclusion, the size of an atom does not directly affect its electric field energy, but it can indirectly influence it by affecting the distribution of charge within the atom.

## What is electric field energy?

Electric field energy is the potential energy that is stored in an electric field due to the presence of electric charges.

## How is electric field energy calculated?

The electric field energy can be calculated by multiplying the electric field strength by the distance between the charges and then dividing by a factor of 2.

## What is the unit of electric field energy?

The unit of electric field energy is joules (J) in the SI system.

## What factors affect the amount of electric field energy?

The amount of electric field energy is affected by the magnitude of the electric charges, the distance between the charges, and the medium in which the charges are located.

## How is electric field energy related to electric potential energy?

Electric field energy and electric potential energy are closely related, as changes in electric field energy result in changes in electric potential energy and vice versa. Electric potential energy is the potential energy of a charge at a certain point in an electric field, while electric field energy is the total potential energy of all charges in an electric field.

• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
12
Views
321
• Introductory Physics Homework Help
Replies
9
Views
7K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
26
Views
921
• Introductory Physics Homework Help
Replies
1
Views
911
• Introductory Physics Homework Help
Replies
1
Views
2K