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 \[\therefore \] \[n=\frac{1}{9\times {{10}^{9}}}\times \frac{{{(0.1)}^{2}}\times (0.036)}{1.6\times {{10}^{-19}}}\] \[n=2.5\times {{10}^{5}}\]You need to login to perform this action.
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