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Q.

A line charge of charge density $λ$ lies along the x-axis and let the surface of zero potential passes through (0, 5, 12) m. The potential at point (1, 3, -4)m is

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a

$\frac{λ}{2 π ε_{0}} \log_{e} (\frac{13}{5})$

b

$\frac{2 λ}{π ε_{0}} \log_{e} (\frac{13}{3})$

c

$\frac{λ}{4 π ε_{0}} \log_{e} (\frac{13}{5})$

d

None of these

answer is A.

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Detailed Solution

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$V_{f} - V_{i} = \frac{λ}{2 π ε_{0}} \log (\frac{r_{f}}{r_{i}})$

here $r$ is the radial distance from the wire in z-y plane.

$\Rightarrow V = - \frac{λ}{2 π ε_{0}} \log_{e} (\frac{\sqrt{3^{2} + 4^{2}}}{\sqrt{5^{2} + 12^{2}}})$

$\Rightarrow V = - \frac{λ}{2 π ε_{0}} \log_{e} (\frac{5}{13})$

$\Rightarrow V = \frac{λ}{2 π ε_{0}} \log_{e} (\frac{13}{5})$

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A line charge of charge density λ lies along the x-axis and let the surface of zero potential passes through (0, 5, 12) m. The potential at point (1, 3, -4)m is