Conductors...?

Question

Two flat conductors are placed with their inner faces separated by 5mm. If the surface charge density on one of the inner faces is 32 pC/M^2 and the other inner face -32pC/m^2, what is the magnitude of the eletric potential difference between the two conductors in volts?

Answer 1

A flat plate conductor (large) when charged spreads the charge uniformly over its entire surface. Except near its boundaries, the surface charge density is uniform. The electric field near such a conductor is always normal to its surface and constant

E = sigma/2 epsilon

where sigma= charge density and
epsilon= permittivity of free space= 8.85 * 10^-12 (MKS)

Two such conductors form a parallel assembly, separated by small distance (in comparison to their size), and are entailing positive and negative charge densities on facing inner surfaces, the electric field :

(E)outside = 0
(E)inside or center = [+sigma/2 epsilon] - [ - sigma/2 epsilon]

(E)in = sigma/ epsilon (constant)

Potential Diff. of 2 conductor = (E)in * separation

sigma= 32*10-12 C/M^2, d = 5mm = 0.005 M
epsilon= 8.854 * 10^-12 C^2/(N*M^2)

V1 -V2 = sigma * d / epsilon

=32*10-12 *0.005 / 8.854 * 10^-12 (N-M/C)
=32*0.005 / 8.854 Volts
=0.01807 volts
answer