Graphene consists of a 2D network of carbon atoms just one atom thick. This simp

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

part 1:

due to symmetrical nature of the placement of charges, electric field due to each charge will cancel out electric field due to the charge diametrically opposite to it

hence total electric field at the center will be 0.

part 2:

let side of the hexagon is d .

charge on each vertex of the hexagon is q.

then numbers of pairs with distance of d in between =6

number of pairs with distance of sqrt(3)*d in between=6

number of pairs with distance of 2*d in between=3

so total electrical potential energy=(k*q*q)*(6*(1/d)+6*(1/(sqrt(3)*d)+3*(1/(2*d))

where k=coloumb's constant

total electric potential energy=(k*q^2)*(10.964/d)

=10.964*k*q^2/d

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