How To apply Gauss’s Law

distribution of electric charge inside the surface

Electric field through surface

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Using gauss’s law you can find

Using gauss’s law you can find

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OBSERVATION #1

Gauss’s law is most useful where charge distribution has symmetry for example spherical symmetry or cylindrical symmetry.

In Symmetrical situations you can find direction of field using symmetry of charge distribution.

You can start analysis of your problem by finding the symmetry of charge distribution first

OBSERVATION #2

After symmetry next step would be to select the Gaussian surface.

Usually integral in Gauss’s law can be evaluated if Gaussian surface and charge distribution have some symmetry.

So you need to choose your Gaussian surface according to the distribution of charge that is choose cylindrical surface for infinitely long line of uniform charge and infinitely long cylinder of uniform charge

OBSERVATION #3After choosing Gaussian surface

you can now carry out the integral in Gauss’s Law

Closed Gaussian surface can be imagined to be made up of number of portions and integral over entire surface would be equal to sum integral over each portion.

If is at right angles to a surface of area A at all points and has same magnitude at all points of the surface , then

and

If electric field is perpendicular and points along inwards direction then

and

If field is parallel to the surface at all points then integral would be zero.

Also if field is equal to zero at all points of the surface then also integral in Gauss’s Law would be equal to zero