A) \[-6a{{\varepsilon }_{0}}r\]
B) \[-24\pi a{{\varepsilon }_{0}}\]
C) \[-6a{{\varepsilon }_{0}}\]
D) \[-24\pi a{{\varepsilon }_{0}}r\]
Correct Answer: C
Solution :
[c] Electric field \[E=-\frac{d\phi }{dr}=-2ar\] ....(i) By Gauss's theorem \[E=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{{{r}^{2}}}\] ?.(ii) From(i) and (ii), Q\[=-8\,\pi {{\varepsilon }_{0}}a{{r}^{3}}\] \[\Rightarrow \]\[dq=-24\pi {{\varepsilon }_{0}}a{{r}^{2}}dr\] Charge density, \[\rho =\frac{dq}{4\pi {{r}^{2}}dr}=-6{{\varepsilon }_{0}}a\]
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