In infinite long uniformly charged string is placed along z- axis. Its linear charge density is λ .

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1. Electric Charges and Fields

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In infinite long uniformly charged string is placed along $z-$ axis. Its linear charge density is $\lambda $. A point charge $q$ is moved from position $(a, 0, 0)$ to $(2a, 0, 0)$ then work done will be

A

$ - \frac{{K\lambda }}{a}\left( q \right)$

B

$\frac{{K\lambda q}}{{2a}}\,\ln \,\left( 2 \right)$

C

$ - 2k\lambda q\,(\ln \,2)$

D

$ - \frac{{2k\lambda q}}{a}\,(\ln \,2)$

Solution

$E= \frac{2 \mathrm{k} \lambda}{\mathrm{r}} $

$ \mathrm{W}_{\mathrm{ext}} =-\Delta \mathrm{u}=-\int \overrightarrow{\mathrm{F}} \cdot \mathrm{d} \overrightarrow{\mathrm{r}} $

$=-\int_{\mathrm{a}}^{2 \mathrm{a}} \overrightarrow{\mathrm{E}} \cdot \mathrm{d} \overrightarrow{\mathrm{r}}$

$ = – 2{\rm{K}}\lambda {\rm{q}}{(\ln {\rm{x}})^{2{\rm{a}}}}$

$ = – 2{\rm{K}}\lambda {\rm{q}}\left( {{\rm{ln2}}} \right)$

Standard 12

Physics

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