A) \[\frac{18}{34}\]
B) \[\frac{18}{54}\]
C) \[\frac{21}{34}\]
D) \[\frac{9}{17}\]
Correct Answer: D
Solution :
[d] \[{{E}_{A}}=\frac{\sigma \left( R/2 \right)}{3{{\varepsilon }_{0}}}=\left( \frac{\sigma R}{6{{\varepsilon }_{0}}} \right)\] \[{{E}_{B}}=\frac{\sigma R}{3{{\varepsilon }_{0}}}-\left( \frac{1}{4\pi {{\varepsilon }_{0}}} \right)\frac{\left( \sigma \right)}{{{\left( \frac{3R}{2} \right)}^{2}}}\frac{4\pi }{3}{{\left( \frac{R}{2} \right)}^{3}}\] \[=\frac{\sigma R}{3{{\varepsilon }_{0}}}-\frac{\sigma R}{54{{\varepsilon }_{0}}}\] \[\Rightarrow {{E}_{B}}=\frac{17}{54}\left( \frac{\sigma R}{{{\varepsilon }_{0}}} \right)\] \[\left| \frac{{{E}_{A}}}{{{E}_{B}}} \right|=\frac{1\times 54}{6\times 17}=\left( \frac{9}{17} \right)\]You need to login to perform this action.
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