Name: Electric Field Produced by a Dipole
Uploaded: 2019-07-19
Duration: 32 min 17 s
Description: What is the electric field of a dipole? Watch the video to understand how the vector addition can be used to determine the electric field of a dipole.

Question

Use Gauss's law to obtain the expression for the electric field due to a uniformly charged infinite plane sheet.

Accepted Answer

Electric field due to a uniformly charged infinite plane sheet :

Consider an infinitely thin plane sheet of positive charge with a uniform charge density $σ$ as shown in the figure.

Let a $P$ point be at a distance from the sheet at which the electric field is required.

The cross-section area of the gaussian cylinder is $A$ .

electric flux crossing the gaussian surface.

$ϕ = E \times$ area of cross-section of the gaussian cylinder.

Here, the electric field lines of force are parallel to the curved surface area of the cylinder, the flux due to the electric field of the plane sheet of charge passes only through two circular sections of the cylinder.

$ϕ = E \times 2 A \dots (1)$

According to Gauss's theorem,

$ϕ = \frac{q}{ε_{0}}$

Here, charged enclosed by the gaussian surface,

$q = σ A$

$ϕ = \frac{σ A}{ε_{0}} \dots (2)$

From the $(1) & (2)$

$E \times 2 A = \frac{σ A}{ε_{0}}$

$E = \frac{σ}{2 ε_{0}}$

Use Gauss's law to obtain the expression for the electric field due to a uniformly charged infinite plane sheet.

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