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Question
A non-conducting sheet of large surface area and thickness d contains a uniform charge distribution of density ρ. Find the electric field at a point P inside the plate, at a distance x from the central plane. Draw a qualitative graph of E against x for 0 < x < d.
Solution
Given:
Thickness of the sheet = d
Let the surface area of the sheet be s.
Volume of the sheet = sd
Volume charge density of the sheet, ρ = `"Q"/"sd"`
Charge on the sheet = Q
Consider an imaginary plane at a distance x from the central plane of surface area s.
Charge enclosed by this sheet, q =ρsx
For this Guassian surface, using Gauss's Law,we get:
`oint "E"."ds" = "q"/∈_0`
`"E"."s" = (ρ "sx")/∈_0`
`"E" =( ρ "x")/∈_0`
The electric field outside the sheet will be constant and will be:
`"E" =(ρ"d")/∈_0 `
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