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) \[-\,\frac{\lambda }{2\pi {{\in }_{0}}}\,\,\ell n\,\,\frac{13}{5}\]

Correct Answer: A

Solution :

[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 \[(2,3,-\,4)=\frac{\lambda }{2\pi {{\in }_{0}}}\,\,In\,\,\frac{13}{5}\]