A) \[10\,\mu V\]
B) \[20\,\mu V\]
C) \[30\,\mu V\]
D) \[40\,\mu V\]
Correct Answer: C
Solution :
[c] EMF induced in an element of length dx at a distance x from wire =\[Bvdx\] \[\therefore \] Total EMF induced in the rod \[E=\int\limits_{0.01}^{0.2}{Bv}\,\,dx=\int\limits_{0.01}^{0.2}{\frac{{{\mu }_{0}}iv}{2\pi x}}\] \[dx=\frac{{{\mu }_{0}}iv}{2\pi }\,\,\] \[\int\limits_{0.01}^{0.2}{\frac{1}{x}}\,dx\] \[E=\frac{{{\mu }_{0}}iv}{2\pi }\left[ {{\log }_{e}}x \right]_{0.01}^{0.2}=\frac{{{\mu }_{0}}iv}{2\pi }[{{\log }_{10}}(0.2)-{{\log }_{10}}\] \[(0.01)]\times 2.303\] \[E=\frac{4\pi \times {{10}^{-7}}\times 5\times 10}{2\pi }[1.301]\times 2.303\] \[=2.99\times {{10}^{-5}}\,V\approx 30\mu V\]
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