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The electric field in a region is radial...

The electric field in a region is radially outward with magnitude `E=Aa`. Find the charge contained in a sphere of radius a centred at the origin. Take `A=100 V m^(-2)` and `a=20.0 cm`.

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The electric field at the surface of the sphere is Aa and being radial it is along the outward normal. The flux of the electric field is. Therefore,
` Phi=oint E dS costheta=Aa*4pia^2)`.
The charge contained in the sphere is, from Gauss's law,
`Q_inside= epsilon_0 phi=4piepsilon_0 Aa^2`
`= {1/9 xxx 10^9 C^2 N^(-1) m^(-2) (100 V m^(-2) (0.20m)^3`
`=8.89 xx 10^(-11) C.
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