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 :
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a
Aε0a2
b
4πε0Aa3
c
ε0Aa3
d
4πε0Aa2
answer is B.
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Detailed 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 4πa3Now according to Gauss's lawϕ=qinε0⇒qin=ϕ.ε0So, qin=A4πa3ε0