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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' centered at the origin of the field, will be given by:

Aε₀a²

4πε₀Aa²

4πε₀Aa³

ε₀Aa³

Solution:

From Gauss's law, ∮→E⋅→dS=qenc/ε₀
At r=a, E=Aa
∴∮→E⋅→dS = (Aa)4πa² = qenc/ε₀
→qenc = 4πε₀Aa³