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susdu
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Homework Statement
Describe the potential inside and outside an infinite insulating sheet with uniform density ρ and thickness d, as a function of x (distance from the center of the sheet). zero potential has been set at its center. What is the potential on the surface of the sheet?
Homework Equations
Potential and E.field definitions.
The Attempt at a Solution
I know that inside the sheet ([itex] x<\frac{d}{2}[/itex]) the field is given by
[itex] E=\frac{ρx}{ε_0}[/itex].
so, potential inside the sheet (with ##V_i=0## at ## x=0##) is:
##V_f=-\int^x_0 E\,ds=-\frac{ρx^2}{ε_0}##
similarly, outside the sheet ([itex] x>\frac{d}{2}[/itex]) field is
[itex] E=\frac{ρd}{ε_0}[/itex].
however, I'm not sure about the expression for outside the sheet, is it
##V_f=-\int^\frac{d}{2}_0 E\,ds-\int^x_\frac{d}{2} E\,ds##
?