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If electric field in a region is radially outward with magnitude E = Ar, the charge contained in a sphere of radius r centred at the origin is

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a

$4 π ε_{0} A r^{3}$

b

$\frac{1}{4 π ε_{0} r^{3}}$

c

$\frac{4 π ε_{0} A}{r^{3}}$

d

$\frac{1}{4 π ε_{0}} A r^{3}$

answer is B.

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Detailed Solution

$E = \frac{q}{4 π ε_{0} r^{2}} \Rightarrow A r = \frac{q}{4 π \in_{0} r^{2}} \Rightarrow q = 4 π ε_{0} A r^{3}$

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If electric field in a region is radially outward with magnitude E = Ar, the charge contained in a sphere of radius r centred at the origin is