A) \[7.27\times {{10}^{-4}}\,C/m\]
B) \[7.98\times {{10}^{-4}}\,C/m\]
C) \[7.11\times {{10}^{-4}}\,C/m\]
D) \[7.04\times {{10}^{-4}}\,C/m\]
Correct Answer: B
Solution :
Relation for electric field is given by \[E=\frac{\lambda }{2\pi {{\varepsilon }_{0}}r}\] (Given :\[~E=\text{ }7.182\times {{10}^{8}}N/C\]) \[r=\text{ }2cm=\text{ }2\times {{10}^{2}}m\] \[\frac{1}{4\pi {{\varepsilon }_{0}}}=9\times {{10}^{-9}}\] Þ \[\lambda =2\pi {{\varepsilon }_{0}}rE=\frac{2\times 2\pi {{\varepsilon }_{0}}rE}{2}\] \[=\frac{1\times 2\times {{10}^{-2}}\times 7.182\times {{10}^{8}}}{2\times 9\times {{10}^{9}}}=7.98\times {{10}^{-4}}C/m\]
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