Question

Figure represent an infinite sheet of charge of surface charge density σ. You have to find electric field intensity at P due to this infinite charge.

1. Can you apply Coulomb’s inverse square law to find electric field at P? 

2. Find electric field intensity at P due to this sheet

Answer 1

1. No.

2. Field due to A uniformly charged infinite plane sheet:

Consider an infinite thin plane sheet of change of density σ.

To find electric field at a point P (at a distance ‘r’ from sheet), imagine a Gaussian surface in the form of cylinder having area of cross section ‘ds’. 

According to Gauss’s law we can write,

But electric field passes only through end surfaces ,so we get ∫ds = 2ds

i.e. E 2ds  = \(\frac{\sigma ds}{\varepsilon_0}\)

E = \(\frac{\sigma ds}{2ds\varepsilon_0},\) \(E =\frac{\sigma}{2\varepsilon_0}\)

E is directed away from the charged sheet, if σ is positive and directed towards the sheet if σ is negative.