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Gauss`s law

Nagendra chowdary asked : –

“A circular ring of radius r made of a non conducting material is placed with its axis is parallel to a uniform electric field if the ring rotated by 180 degrees Does the flux changes? A Q charge is uniformly distributed on a thin spherical shell If a point charge is brought near it what is the field at the center?Is u r answer depends on whether it is conducting or non conducting?”

A Question from Electric Flux and Gauss Theorem

Zeenath asked:

How can you prove that dS in φ =E.dS is dS Cos θ if the area is tilted at an angle ? I need the mathematical Steps.

 

Ans;

Dear Zeenath,
Electric Flux is defined as the total no of field lines passing normal to the surface. So while calculating, we need to consider the area of the surface normal to the field lines only. That is why we take the dot product of E and ds, where ds is the area vector (not just the area: Area vector is a vector whose magnitude is equal to the area and dirtected normal to the surface.)
Then by definition of dot product,
dφ =E.dS = EdS cos θ
which gives the component of E and the component of area vector in the direction of E (When area vector is in the direction of E, the actual component of area is perpendicular to E)
Hope the matter is clear.
Mathew Abraham

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