A)
\[2\times {{10}^{-7}}\,N/m\] B)
\[2\times {{10}^{-8}}\,N/m\]
C)
\[5\times {{10}^{-8}}\,N/m\]
D)
\[{{10}^{-7}}\,N/m\]
Correct Answer:
A Solution :
\[\frac{F}{l}=\frac{{{\mu }_{0}}}{2\pi }\times \frac{{{i}_{1}}\,\,{{i}_{2}}}{r}\] where \[{{i}_{1}}\] and \[{{i}_{2}}\] are the currents in wires 1 and 2 respectively and r is the distance between them. Since, it is given that between two wires, there is a force of attraction, so the direction of currents in both will be the same. Here, \[{{i}_{1}}={{i}_{2}}=1\,A,\,r=1\,m,\] \[{{\mu }_{0}}=4\pi \times {{10}^{-7}}\,T-m/A\] \[\therefore \] \[\frac{F}{l}=\frac{4\pi \times {{10}^{-7}}}{2\pi }\times \frac{1\times 1}{1}\] \[=2\times {{10}^{-7}}\,N/m\]
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