Name: Introduction to Electric Charge
Uploaded: 2019-07-19
Duration: 9 min 41 s
Description: In this video, we will study electric charge and its properties and we will also learn about different methods of charging.

Question

Write the statement of Gauss's law for electrostatics. Derive an expression for electric field due to an uniformly charged infinite non-conducting sheet at a point near to it. Draw suitable diagram.

Accepted Answer

Gauss Theorem: The net outward electric flux through a closed surface is equal to 1/ε0 times the net charge enclosed within the surface i.e.,

$\oint \vec{E} . \vec{d s} = \frac{1}{ε_{0}} \sum q$

Let electric charge be uniformly distributed over the surface of a thin, non-conducting infinite sheet. Let the surface charge density (i.e., charge per unit surface area) be s. We have to calculate the electric field strength at any point distance r from the sheet of charge.

To calculate the electric field strength near the sheet, we now consider a cylindrical Gaussian surface bounded by two plane faces A and B lying on the opposite sides and parallel to the charged sheet and the cylindrical surface perpendicular to the sheet (fig). By symmetry the electric field strength at every point on the flat surface is the same and its direction is normal outwards at the points on the two plane surfaces and parallel to the curved surface. Total electric flux.

$\oint \vec{E} . d \vec{s} = \oint \vec{E} . d \vec{s_{1}} + \oint \vec{E} . d \vec{s_{2}} + \oint \vec{E} . d \vec{s_{3}} \oint \vec{E} . d \vec{s} = \int E d s_{1} \cos 0 ° + \int E d s_{2} \cos 0 ° + \int E d s_{3} \cos 90 ° = E \int d s_{1} + E \int d s_{2} = E a + E a ∴ t o t a l e l e c t r i c f l u x = 2 E a$

As $σ$ is charge per unit area of sheet and a is the intersecting area, the charge enclosed by Gaussian surface = $σ a$

According to Gauss’s theorem,

Total electric flux= $\frac{1}{ε_{0}} (σ a)$

$2 E a = \frac{1}{ε_{0}} \times σ a E = \frac{σ}{2 ε_{0}}$

Thus, electric field strength due to an infinite flat sheet of charge is independent of the distance of the point and is directed normally away from the charge. If the surface charge density σ is negative the electric field is directed towards the surface charge.

Write the statement of Gauss's law for electrostatics. Derive an expression for electric field due to an uniformly charged infinite non-conducting sheet at a point near to it. Draw suitable diagram.

Important Questions on Electric Charges and Fields

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