First slide
Electric Flux
Question

The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius 'a' centred at the origin of the field, will be given by :

Moderate
Solution

Flux linked with sphere = E.d s

Since electric field is radial. It is always perpendicular to the surface.

So  ϕ=Ar.4πr2

     ϕ=Aa4πr2    as r=a ϕ=A 4πa3

Now according to Gauss's law

ϕ=qinε0qin=ϕ.ε0

So, qin=A4πa3ε0

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