Question

Use gauss law to find the due to a uniformly charged infinite plane sheet what is the of the field for positive and negative charge density

Answer 1

Let us consider two uniformly charge parallel sheets carrying surface charge densities +0> and — CT respectively and are separated by a small distance from each other.

By Gauss’ law, it can be proved that, electric field intensity due to a uniformly charged infinite plane sheet as nearby is given by

The electric field is directed normally outward from the plane sheet, if nature of charge on sheet is positive and normally inward, if charge is of negative nature. Let ? represents unit vector directed from positive plate to negative plate.

Now, electric field intensity (EFI) at any point P between the two plates is given by

Answer 2

✯ Question Given :

• ➥ Use gauss law to find the Electric fields due to a uniformly charged infinite plane sheet what is the of the field for positive and negative charge density ?

✯ Required Solution :

• ➥ let electric charge be uniformly distributed over the surface of things non - conducting infinite sheet. Let the surface charge density be σ [ Sigma ]

★ According to Gauss Theorum :

• [ Before solving ahead go through the diagram given in attachment ]

• ➢ ∫E. ds + ∫E.ds + ∫E.ds = q / ε₀

(1) (2) (3)

• ➢ ∫E. dsCos0° + ∫E.dsCos0° + ∫E.dsCos90° = q / ε₀

• ➥ [ Cos90° = 0 ] , [ Cos0° = 1 ]

• ➢ ∫Eds + ∫Eds = q / ε₀

• ➢ 2∫Eds = q / ε₀

• ➢ 2E.S = σS / ε₀

• ➢ E = σ / 2 ε₀

✯ Therefore :

• ➥ Electric fields due to a uniformly charged infinite plane sheet is E = σ / 2 ε₀

_______________________