• question_answer A infinitely long line charge of charge density $\lambda$ lies along the x axis and let the surface of zero potential passes through (0, 5, 12) m. The potential at point $(2,3,-\,4)$ is - A) $\frac{\lambda }{2\pi {{\in }_{0}}}\,\,\ell n\,\,\frac{13}{5}$        B) $\frac{2\lambda }{\pi {{\in }_{0}}}\,\,\ell n\,\,\frac{13}{3}$ C) $\frac{\lambda }{4\pi {{\in }_{0}}}\,\,\ell n\,\,\frac{13}{5}$        D) $-\,\frac{\lambda }{2\pi {{\in }_{0}}}\,\,\ell n\,\,\frac{13}{5}$

[A] Perpendicular distance of A (0, 5, 12) from x axis$={{r}_{1}}=13$ & $B=(2,3,-\,4)$ from x axis ${{r}_{2}}=5$ and potential difference between these two point is $=\frac{\lambda }{2\pi {{\in }_{0}}}$ In $\frac{13}{5}$ ${{V}_{B}}-{{V}_{A}}=\frac{\lambda }{2\pi {{\in }_{0}}}\,\,In\,\,\frac{13}{5}$ ${{V}_{A}}=0$ $\therefore \,\,\,{{V}_{B}}=\frac{\lambda }{2\pi {{\in }_{0}}}\,\,In\,\,\frac{13}{5}$ Potential at $(2,3,-\,4)=\frac{\lambda }{2\pi {{\in }_{0}}}\,\,In\,\,\frac{13}{5}$
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