A) 1.5 \[Ao\]
B) 2.25 \[Ao\]
C) 0.5 \[Ao\]
D) 0.25 \[Ao\]
Correct Answer: C
Solution :
Force between two straight parellel wire is given by \[F=\frac{{{\mu }_{0}}\times {{i}_{1}}{{i}_{2}}l}{2\pi \times r}=\frac{{{\mu }_{0}}}{2\pi }\times \frac{{{i}^{2}}\times l}{r}\] ?(i) \[\left( \begin{align} & \text{Given:}{{i}_{1}}={{i}_{2}},r=0.15m \\ & F=30\times {{10}^{-7}}N,l=9m \\ \end{align} \right)\] Now, putting the given values in Eq. (i) \[30\times {{10}^{-7}}=\frac{4\pi \times {{10}^{-7}}\times {{i}^{2}}\times 9}{2\pi \times 0.15}\] or \[{{i}^{2}}=\frac{30\times {{10}^{-7}}\times 0.15}{2\times {{10}^{-7}}\times 9}=0.25=\frac{1}{4}\] \[i=\sqrt{\frac{1}{4}}=\frac{1}{2}=0.5A\]
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