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Question
Using Gauss’s law, prove that the electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it.
Solution
Consider a uniformly charged infinite plane sheet of charge density σ.
We have to find electric field E at point as shown in figure.
Now, we construct a Gaussian surface as shown in figure in the form of cylinder.
Applying Gauss’s Law,
`phi =oint vecE*dvecs =(σΔs)/in_0`
`=> E Deltas + EDelta +0 = (sigma Deltas)/in_0`
`= 2EDeltas = (sigma Deltas)/(in_0)`
`=> E = sigma /(2in_0)`
It shows that electric field is uniform due to charged infinite plane sheet. Also, we can say that E is independent from distance from the sheet.
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