Question

state the theorem which relates the enclosed charge inside a closed surface with surface integral of a electric field . Use this theorem to obtain the electric field due to an infinite plane sheet of charge


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Answer 1

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Answer 2

Answer

Gauss Law for electrostatics states that the total electric flux passing through a closed surface equals the enclosed charge in the surface divided by the permittivity of the medium.

ϕ E =∮( E ⋅ dS )= ε oQ

enclosed

Consider an infinite plane sheet of positive charge with charge density σ as shown in the attached figure. Electric field lines will be directed orthogonal and away from the sheet of charge. Hence, a cylindrical closed surface with its base parallel to the sheet of paper as shown in the figure is a good choice of Gaussian surface.

For the curved surface electric field is orthogonal to the surface area vector. Hence, flux linked to curved surface is zero.

ϕ S =0................(i)

For the plane surface, applying Gauss's Law, we get:

ϕ s +ϕ b = ε oQ

enclosed

EA+EA= ε oQ

enclosed

But Q=σA by definition of surface charge density

⟹E= 2ε oσ

It should be noted that for an infinite line sheet of charge, electric filed does not depend on the distance of the point from the surface.

Explanation:

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