Answer is (i) Zero
Let \(F_1\) is force per unit, length between A & C
i.e. \(F_1 = \frac{\mu_0}{2\pi}\frac{2I\times I}{2r}\)
And \(F_2\) is force per unit, length between B & C
\(F_2=\frac{\mu_0}{2\pi}\frac{I\times I}r\)
Now net force on ‘C’ is per unit length
\(F_1+F_2=\frac{\mu}{2\pi}\frac{I^2}r(1+1)\)
\(=\frac{2\mu_0}{2\pi}\frac{I^2}r\) = F(given)
Now Fig b
\(F'_1\) = Repulsive force between A & C
\(=\frac{\mu_0}{2\pi}\frac{2I^2}{2r}\)
\(F'_2=F_2\) = A reactive force between B & C
\(\therefore\) Net force on 'C' \(F'_1-F'_2=0\)
\(F'_1=F'_2=\frac{\mu}{2\pi}\frac{2I^2}{2r}\)
\(\therefore\) Net Force on ‘C’ is zero.