A) \[\frac{C{{R}^{3}}}{20{{\in }_{0}}}\]
B) \[\frac{C{{R}^{3}}}{10{{\in }_{0}}}\]
C) \[\frac{C{{R}^{3}}}{5{{\in }_{0}}}\]
D) \[\frac{C{{R}^{3}}}{40{{\in }_{0}}}\]
Correct Answer: D
Solution :
[d] For, \[r=R/2\] Using Gauss's law, we have \[\oint{\vec{E}.d\vec{A}=\frac{{{q}_{in}}}{{{\varepsilon }_{0}}}\text{ or }E\times 4\pi {{r}^{2}}=\int\limits_{0}^{R/2}{\frac{\rho 4\pi {{r}^{2}}dr}{\varepsilon {{ & }_{0}}}}}\] \[\text{or }E=\frac{C{{r}^{3}}}{5{{\in }_{0}}}=\frac{C{{R}^{3}}}{40{{\in }_{0}}}.\]You need to login to perform this action.
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