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# A particle of mass m and charge q is connected to a vertical and infinitely long line-charge of linear charge density $\lambda$ by an insulating, inextensible, and mass less string of length l.Taking $k =\large\frac{\lambda q}{2 \pi \in_0 /mg}$ , the angle $\theta$ made by the string with the line charge will be

$\; \cos ^{-1} \bigg( \large\frac{-k +\sqrt {k^2+4}}{2} \bigg )$ is correct.
Hence A is the correct answer.