question_answer

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                           

A)  \[4\pi {{\varepsilon }_{0}}A{{a}^{2}}\]         

B)  \[A{{\varepsilon }_{0}}{{a}^{2}}\]           

C)                         \[4\pi {{\varepsilon }_{0}}A{{a}^{3}}\]      

D)   \[{{\varepsilon }_{0}}A{{a}^{3}}\]

Correct Answer: C

Solution :

                Given, Here,             r = a \[E=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{{{a}^{2}}}\] From Eq. (i), \[\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{{{a}^{2}}}=Aa\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,q=4\pi {{\varepsilon }_{0}}A{{a}^{3}}\]