Question

application of gauss theroum

Answer 1

Heya user☺

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Applications of Gauss’s Law

Gauss’s Law can be used to solve complex electrostatic problems involving unique symmetries like cylindrical, spherical or planar symmetry. Also, there are some cases in which calculation of electric field is quite complex and involves tough integration. Gauss’s Law can be used to simplify evaluation of electric field in a simple way.

We apply Gauss’s Law in following way:

Choose a Gaussian surface, such that evaluation of electric field becomes easy

Make use of symmetry to make problems easier

Remember, it is not necessary that Gaussian surface to coincide with real surface that is, it can be inside or outside the Gaussian surface

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Answer 2

Hi there!

GAUSS'S LAW in simplified form can be written as under, E = q(in) / €.

APPLICATIONS OF GAUSS'S LAW--
As Gauss's law doesn't provide expression for electric field but provides only for it's flux through a closed surface. To calculate E we choose an imaginary closed surface (called Gaussian surface) in which the above equation can be applied easily.
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Let's discuss few simple cases-->

(1). ELECTRIC FIELD DUE TO A POINT CHARGE:
The electric field due to a point charge is everywhere radial. We wish to find the electric field at a distance r from the charge q. We select Gaussian surface a sphere at distance r from the charge. At every point of the sphere the electric field have the same magnitude E and it is perpendicular to the surface itself. Hence, we can apply the simplified form of Gauss's law,

(refer to attachment).
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(2). ELECTRIC FIELD DUE TO A LINEAR CHARGE DISTRIBUTION:
Consider a long line charge with the linear charge density (charge per unit length) Lambda. We have to calculate the electric field at a point, a distance r from the line charge. We construct a Gaussian surface, a cylinder of any arbitrary length l of radius r and its axis coinciding with the axis of the line charge. This cylinder have 3 surfaces. One is curved surface and the two plane parallel surfaces field lines at plane parallel surfaces are tangential (so flux passing through these surfaces is zero). The magnitude of electric field is having the same magnitude (say E) at curved surface and simultaneously the electric field is perpendicular at every point of the surface. Hence we can apply the Gauss's law here.
(refer to the attachment).

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(3). ELECTRIC FIELD DUE TO A PLANE SHEET OF CHARGE:
The figure in the given attachment shows a portion of a flat thin sheet, infinite in size with constant surface charge density Sigma ( charge per unit area). By symmetry, since the sheet is infinite, the field must have the same magnitude and the opposite direction at two points equidistant from the sheet on opposite sides. Let us draw a Gaussian surface (a cylinder) with one end on one side and other end on the other side and of cross sectional area S. At plane surfaces electric field has same magnitude and perpendicular to surface.

(refer to the attachment).

Thus, we see that the magnitude of the field is independent of the distance from the sheet. Practically, an infinite sheet of charge does not exist. The result is correct for real charge sheet if. Under consideration are not near the edges and the distances from the sheet are small compared to the dimensions of sheet.
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(4). ELECTRIC FIELD NEAR A CHARGED CONDUCTING SURFACE:
When a charge is given to a conducting plate, it distributes itself over the entire outer surface of the plate. The surface density Sigma is uniform and is the same on both surfaces if plate is of uniform thickness and of infinite size.
This is similar to the previous one, the only difference is that this time charges are on both sides.

(refer to the attachment).

Thus, field due to a charged conducting plate is twice the field due to plane sheet of charge.
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Hope it helps!