A) \[5.48\text{ }V/m\]
B) \[7.75\text{ }V/m\]
C) \[1.73\text{ }V/m\]
D) \[2.45\text{ }V/m\]
Correct Answer: D
Solution :
[d] Using \[{{U}_{av}}=\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}\] But \[{{U}_{av}}=\frac{P}{4\pi {{r}^{2}}\times c}\] \[\therefore \,\,\,\,\,\frac{P}{4\pi {{r}^{2}}}=\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}\times c\Rightarrow E={{\left( \frac{2P}{4\pi {{\varepsilon }_{0}}}\times \frac{1}{c{{r}^{2}}} \right)}^{\frac{1}{2}}}\] \[\Rightarrow \,\,\,\,\,\,\,E={{\left( 2\times 9\times {{10}^{9}}\times \frac{0.1}{3\times {{10}^{8}}\times 1\times 1} \right)}^{\frac{1}{2}}}\] \[=\sqrt{6}\,=2.45\,\,V/m\]
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