Question

Long Answer Type Questions :
Q. 1. State the Theorem which relates the enclosed charge inside a closed surface
with surface integral of Electric field. Use this theorem to obtain the electric
field due to an infinite plane sheet of charge,​

Answer 1

Answer:

Explanation:Gauss' theorem states that the total electric flux through a closed surface is equal to q / ɛ0 times the magnitude of the charge enclosed. Mathematically, dФ = q/ε0 In other words, Gauss' theorem states that the surface integral of the electric field over the closed surface is equal to 1/ɛ0 times the charge enclosed.

Please mark me as brilliant

Answer 2

Answer:

Gauss Theorem relates the enclosed charge inside a closed surface with surface integral of Electric field. The derivation to obtain the electric field due to an infinite plane sheet of charge was given below

Explanation:

• Gauss Theorem relates the enclosed charge inside a closed surface with surface integral of Electric field.
• The net electric flux will become zero if no charge is enclosed by the surface.
• Therefore, the number of electric lines entering the surface is equal to the number of electric lines leaving the surface.

To obtain the electric field due to an infinite plane sheet of charge, by using the Gauss theorem:

The charge of the thin infinite uniformly charged plane sheet is σ.

A be the area of the cross-section.

The three surfaces of the cylinder are A, S₂, and A'. Therefore, 0 is the electric flux of S₂.

φ = Electric flux through A + Electric flux through S₂ + Electric flux  through A'

φ = E A Cos 0° + 0 + E A Cos 0°

Cos 0° = 1

φ = 2 E A .......................(1)

Using Gauss Theorem:

φ = q / ε₀

φ = σ A / 2 ε₀ ...................(2)

Where q = σ A

Equate the equation (1) and (2) we get,

2 E A = σ A / 2 ε₀

E = σ / 2 ε₀

• The outward direction is for positive field density and is perpendicular to the plane infinite sheet.
• The inward direction is for negative field density and is perpendicular to the sheet.

#SPJ3