Applications of Gauss’ Theorem( Field Due to Thin Infinite Plane Sheet of Charge)

Chapter-1|Electric Charges and Fields | NCERT 12th Physics:

Applications of Gauss’ Theorem:

(II)Field Due to Thin Infinite Plane Sheet of Charge:

We consider a thin, infinite plane sheet of charge with uniform surface charge density Sigma(σ).We want to calculate its electric field at point P, at distance r from it.

Now, to form a Gaussian surface on the sheet we choose cylindrical Gaussian surface of cross sectional area A and length 2r with its perpendicular to the sheet.

 

On the curved surface of the cylinder, E and n^ are perpendicular to each other. Therefore flux through curved surface area=0. Flux through the flat surface = EA+EA=2EA. Total electric flux over the entire surface of the cylinder-

 

 

From above E is independent of r, The distance of the point from the plane charge sheet.

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