question_answer

The number of electrons to be put on spherical conductor of radius 0.1 m, to produce an electric field of 0.036 N/C just above its surface, is:

A) \[3.4\times {{10}^{5}}\]                                

B) \[2.5\times {{10}^{5}}\]

C) \[3.7\times {{10}^{5}}\]                                

D) \[4.7\times {{10}^{5}}\]

Correct Answer: B

Solution :

Total charge on the surface is \[q=ne\]. ..(i) where, n is number and e is electric charge. Also electric field E is given by \[E=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{{{R}^{2}}}\] \[\therefore \]     \[q=4\pi {{\varepsilon }_{0}}{{R}^{2}}E\]            ?(i) Equating Eqs. (i) and (ii), we get  \[ne=4\pi {{\varepsilon }_{0}}{{R}^{2}}E\] \[\Rightarrow \]    \[n=\frac{4\pi {{\varepsilon }_{0}}{{R}^{2}}E}{e}\] Putting this value of R in Eq. (i), we get \[\therefore \]    \[n=\frac{1}{9\times {{10}^{9}}}\times \frac{{{(0.1)}^{2}}\times (0.036)}{1.6\times {{10}^{-19}}}\] \[n=2.5\times {{10}^{5}}\]