A) \[{{V}_{q}}=2{{V}_{p}}\]
B) \[{{V}_{q}}=3{{V}_{p}}\]
C) \[{{V}_{q}}=4{{V}_{p}}\]
D) \[{{V}_{q}}=\left( \frac{1}{4} \right){{V}_{p}}\]
Correct Answer: C
Solution :
\[{{B}_{1}}=\frac{{{\mu }_{0}}}{4\pi }\left( \frac{2\pi {{I}_{1}}}{{{r}_{1}}} \right),B=\frac{{{\mu }_{0}}}{4\pi }\left( \frac{2\pi {{I}_{2}}}{{{r}_{2}}} \right)\] \[{{r}_{2}}=2{{r}_{1}},{{B}_{1}}={{B}_{2}}\]&\[{{I}_{2}}=2{{I}_{1}}\] \[\frac{{{V}_{q}}}{{{V}_{p}}}=\frac{{{I}_{2}}{{r}_{2}}}{{{I}_{1}}{{r}_{1}}}=\frac{2{{I}_{1}}}{{{I}_{1}}}\times \frac{2{{r}_{1}}}{{{r}_{1}}}=\frac{4}{1}\] Hence, the correction option is (c).
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