Page 19 - Electrostatics-11
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© GC Shiba
Gauss Theorem:
Statement: The total electric flux passing through the closed surface of
1
arbitrary shape is equal to times the enclosed charge where ∈ is the
∈ 0 0
permittivity of a free space.
ℎ
∴ =
∈ 0
Let +Q charge enclosed by an arbitrary shape surface is shown in figure.
Total electric flux through this surface is
ℎ
=
∈ 0
∴ =
∈ 0
Proof for spherical surface:
Consider a +Q charge at the center of a sphere of radius r. The electric
intensity at the surface of sphere is
=
4 2
0
1
= Where = 4 = ℎ
2
0
or, E × A =
∈ 0
∴ =
∈ 0
18 Electrostatics
