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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(3) 4πε₀ A a³. The field is radial and has the same magnitude everywhere on a sphere of radius a, so the flux through that sphere is just E times its area: φ=E(a)×4π a²=(Aa)(4π a²)=4π A a³ Gauss's law then gives the enclosed charge: φ=q/(ε₀)⇒ q=ε₀φ=4πε₀ A a³ Notice that the charge grows as a³, so the charge density is uniform - a field rising linearly with r is what a uniformly charged ball produces inside itself.

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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