Periodic images of dipole line charge followed by a vacuum space

[SK2]

Homework Statement

I am trying to calculate the potential due to a dipole line charge placed at the interface of a 2d lateral metal-semiconductor junction followed by vacuum and this system repeats itself as in its a unit cell of metal-semiconductor-vacuum. Could someone help in setting up the equations?

Relevant Equations

A single line charge with constant charge density lambda gives rise to 1/4pi*epsilon0 *lambda*ln(a/r)

Can I sum up the potential due to all positive line charges and all negative line charges separately, with the boundary condition being at the edge of my unit cell, the potential should be the same and inside the metal there is a contant potential?

 

[Nate810]

Yes, you can sum up the potential due to all positive line charges and all negative line charges separately. The boundary condition is that at the edge of your unit cell, the potential should be the same and inside the metal there should be a constant potential.