Electric potential energy in an infinite 2d crystal

In summary, the conversation discusses the calculation of the constant k for a 2D crystal with +-e0 charges in an infinite square net. The formula for k is given and it is noted that it is theoretically impossible to sum an infinite number of terms, but the constant will converge to the final result. The speaker also requests help in calculating this constant and suggests using the "madelung constant" on Wikipedia as a starting point.
  • #1
Istvan
2
0
So.. we've got a 2D crystal, corresponding an infinite square net with +-e0 charges in each one (see the atached photo). Now I'd like to calculate the constant k..when r goes to infinity... We = k (+-e0)*(+-e0)/(4 pi eps0 r)..on the positive charge in the center caused by the negative and positive charges around him in the net. It's teoretically impossible to sum infinite number of terms, but the constant k will converge to the final result. So I'd like some help how to calculate that... thanks.
 

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  • #2
'madelung constant' on wikipedia is a starting point
 
  • #3
thanks

and what is the madelung constant for a 2d arrangement
 

1. What is electric potential energy in an infinite 2d crystal?

Electric potential energy in an infinite 2d crystal refers to the energy that is stored in the crystal as a result of the arrangement of electric charges within it. This energy is a result of the interactions between the charged particles and their surrounding environment.

2. How is electric potential energy calculated in an infinite 2d crystal?

Electric potential energy in an infinite 2d crystal can be calculated using the formula U = Q1Q2/4πεr, where U is the potential energy, Q1 and Q2 are the magnitudes of the charges, ε is the permittivity of the medium, and r is the distance between the charges.

3. What are the factors that affect electric potential energy in an infinite 2d crystal?

The factors that affect electric potential energy in an infinite 2d crystal include the magnitude and sign of the charges, the distance between the charges, and the permittivity of the medium in which the crystal is located.

4. What are the applications of studying electric potential energy in an infinite 2d crystal?

Studying electric potential energy in an infinite 2d crystal has several applications, including understanding the behavior of materials at the atomic level, developing new technologies for energy storage and conversion, and improving the efficiency of electronic devices.

5. How does electric potential energy in an infinite 2d crystal differ from that in a finite crystal?

Electric potential energy in an infinite 2d crystal differs from that in a finite crystal in that an infinite crystal has an infinite number of charges, while a finite crystal has a finite number of charges. This leads to differences in the overall energy and behavior of the two types of crystals.

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