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.

Answer 1

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.