Electrostatic energy of two opposite charges in water and in a vacuum

In summary, the electrostatic energy of two opposite charges e and -e, a distance 7 angstroms apart in water at room temperature, can be expressed as E = lambdaKT/80. In a vacuum, the energy can be expressed as lambdaKT. The Bjerrum length is represented by lambda_B and is calculated using the equation lambda_B k_BT = e^2/(4pi epsilon). The distance between the charges is denoted by r in the equations.
  • #1
JordanGo
73
0

Homework Statement



Compare the electrostatic energy of two opposite charges e and -e, a distance 7 angstroms apart in water at room temperature and that in vacuum (express the energy in terms of Bjerrum length)

Homework Equations



E = 1/(4(p[itex]\pi[/itex][itex]\epsilon[/itex]D)*(-e^2)/r^2 ?

The Attempt at a Solution



First of all is this the right equation to use? If so, is the Bjerrum length the distance between the charges? And for a vacuum is the dialectic constant (D) just 1?
 
Physics news on Phys.org
  • #2
Electrostatic energy is:[tex]E=-\frac{e^2}{4\pi \varepsilon D}[/tex]
Bjerrum length:
[tex]\lambda_B=\frac{e^2}{4\pi \varepsilon k_BT}[/tex]
 
  • #3
So, for water:
E=[itex]\lambda[/itex]KT/80?

And for a vacuum:
[itex]\lambda[/itex]KT?
 
  • #4
No, we have:
[tex]\lambda_B k_BT=\frac{e^2}{4\pi\varepsilon}[/tex]
so put it into formula for energy
 
  • #5
I did do that, D=80 for water and D=1 for a vacuum
 
  • #6
In my formula "D" denotes distance
 
  • #7
Ok that makes sense, so D is dialectric constant and let's say r now is the distance, which is missing in the equations.
 

1. What is electrostatic energy?

Electrostatic energy is the potential energy that exists between two charged particles due to their electric charges. It is a form of potential energy that can be converted into other forms of energy, such as kinetic energy.

2. How does the electrostatic energy of two opposite charges differ in water and in a vacuum?

In water, the electrostatic energy is reduced due to the presence of the polar water molecules. These molecules align themselves with the charges, creating a weaker electric field and decreasing the electrostatic energy. In a vacuum, there are no surrounding molecules to interact with the charges, so the electrostatic energy remains at its maximum.

3. Why is the electrostatic energy of two opposite charges greater in a vacuum?

In a vacuum, there are no surrounding molecules to interact with the charges, so the electrostatic energy remains at its maximum. Without any external forces, the two opposite charges will experience a strong attraction towards each other, resulting in a higher amount of electrostatic energy.

4. How does distance affect the electrostatic energy of two opposite charges?

The electrostatic energy between two opposite charges is directly proportional to the distance between them. As the distance increases, the electrostatic energy decreases. This is because the electric field, which is responsible for the electrostatic energy, weakens as the distance between the charges increases.

5. Can the electrostatic energy of two opposite charges in water be completely eliminated?

No, the electrostatic energy cannot be completely eliminated in water. However, the presence of water molecules can significantly reduce the electrostatic energy, making it harder for the charges to interact with each other. This effect is known as dielectric screening and is commonly used in capacitors to store electric charge.

Similar threads

  • Advanced Physics Homework Help
Replies
2
Views
2K
Replies
9
Views
1K
  • Advanced Physics Homework Help
Replies
5
Views
1K
Replies
19
Views
800
  • Advanced Physics Homework Help
Replies
3
Views
400
  • Advanced Physics Homework Help
Replies
12
Views
3K
Replies
4
Views
325
  • Advanced Physics Homework Help
Replies
2
Views
1K
  • Advanced Physics Homework Help
Replies
3
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
Back
Top