A) \[0.33\times {{10}^{11}}N{{C}^{-1}}\]
B) \[3\times {{10}^{11}}N{{C}^{-1}}\]
C) \[0.66\times {{10}^{11}}N{{C}^{-1~~}}\]
D) \[1.32\times {{10}^{11}}N{{C}^{-1}}\]
Correct Answer: A
Solution :
Charge density of long wire \[\lambda =\frac{1}{3}C-m\] and \[r=18\times {{10}^{-2}}m\] From Gauss theorem \[\oint{\overrightarrow{E}.d\overrightarrow{S}=\frac{q}{\frac{{{e}_{0}}}{{}}}}\] \[E\oint{dS=\frac{q}{{{\varepsilon }_{0}}}}\] or \[E\times 2\pi rl=\frac{q}{{{\varepsilon }_{0}}}\] or \[E=\frac{q}{2\pi {{\varepsilon }_{0}}rl}=\frac{q/l}{2\pi {{\varepsilon }_{0}}r}\] \[=\frac{\lambda \times 2}{2\pi {{\varepsilon }_{0}}r\times 2}=\frac{\lambda \times 2}{4\pi {{\varepsilon }_{0}}r}\] \[=9\times {{10}^{9}}\times \frac{1}{3}\times 2\times \frac{1}{18\times {{10}^{-2}}}\] \[=\frac{1}{3}\times {{10}^{11}}=0.33\times {{10}^{11}}\] \[0.33\times {{10}^{11}}N{{C}^{-1}}\]You need to login to perform this action.
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