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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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$4 {πε}_{0} {Aa}^{3}$

$4 {πε}_{0} {Aa}^{2}$

$ε_{0} {Aa}^{3}$

${Aε}_{0} a^{2}$

answer is D.

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Detailed Solution

Net electric flux emitted from a spherical surface of radius ' a ' is,

$ϕ_{net} = \frac{q_{in}}{ε_{0}} (form Gauss law)$

$ϕ = ES = (Aa) (4 {πa}^{2})$

$∴ (Aa) (4 π a^{2}) = \frac{q_{in}}{ε_{0}}$

$hence, q_{in} = 4 π ε_{0} {Aa}^{3}$

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