An Electromagnetics question?

Question

An infinite charged sheet has a surface charge density of 1x10^(-7) C/m^2. How far apart are the equipotential Surfaces whose potentials differ by 5.0V?

Answer 1

In MKS units, the equation for the relationship between static charge and the E-field is:
grad . E = charge-density/epsilon-0

For a flat geometry such as that:
2*E*area = area*surface-charge-density/epsilon-0
So:
E = 1e-7/(2*epsilon-0)
= 1e-7(2*8.85e-12)
= e5/(2*8.85)
= 5.65e3 V/m

So, if
5 V = E*d
d = 5/E = 5/(5.65) e-3
= 8.86e-4 m
= 0.886 mm

Answer 2

5 meters.

The electric field is constant, hence the potential difference depends linearly on the distance from the sheet (deltaV = E*deltax)