need help in this two question Graphene consists of a 2D network of carbon atoms

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need help in this two question

Graphene consists of a 2D network of carbon atoms just one atom thick. This simple network of atoms results in remarkable physical properties: graphene has higher strength, better thermal conductivity, and greater intrinsic mobility than any other material known. These properties translate into huge technological potential, for example, in transparent electrodes for flatscreen TVs, in fast, energy-efficient transistors, and in ultrastrong composite materials. Hence an enormous global effort is focused on understanding and controlling graphene's properties with the aim of tailoring them for specific applications. Imagine the atoms are charged with a charge q, calculate the electric field in the center of a hexagonal unit. Clearly state any assumptions made. Calculate an expression for the electric potential energy of 6 equally charged particles distributed on the vertices of a hexagon.

Explanation / Answer

Let the side of regular hexagon be a.

Eleectric field at centre =0 (due to symmetry)

Potential energy for a pair of q1 &q2 is given by =k(q1)*(q2)/a;

In hexagon we will have 6 pair seperated by a, 6 pair seperated by 1.732a & 3 pair seperated by 2a.

So, electrical Potential energy = [6/a+6/1.732a+3/2a][Kq^2]

=(10.96*k*q^2)/a

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