A charge Q is distributed over a line of length L. Another point charge q is placed at a dista

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1. Electric Charges and Fields

hard

A charge $Q$ is distributed over a line of length $L.$ Another point charge $q$ is placed at a distance $r$ from the centre of the line distribution. Then the force expericed by $q$ is

$\frac{{qQ}}{{4\pi { \in _0}({r^2} - {L^2})}}$

$\frac{{qQ}}{{4\pi { \in _0}({r^2} - {{(L/2)}^2})}}$

$\frac{{qQ}}{{4\pi { \in _0}{r^2}}}$

$\frac{{qQL}}{{4\pi { \in _0}{r^3}}}$

${\rm{E}} = \int_{{\rm{r – }}\frac{{\rm{L}}}{2}}^{{\rm{r}} + \frac{{\rm{L}}}{2}} {\rm{k}} \lambda {\rm{dx}}/{{\rm{x}}^2}$

$ = \frac{{{\rm{KQ}}}}{{\rm{L}}}\left( { – \frac{1}{{\rm{x}}}} \right)_{{\rm{r – }}\frac{{\rm{L}}}{2}}^{{\rm{r}} + \frac{{\rm{L}}}{2}}$

$=\frac{\mathrm{KQ}}{\left(\mathrm{r}^{2}-(\mathrm{L} / 2)^{2}\right)}$

$\mathrm{F}=\mathrm{q} \mathrm{E}$

Standard 12

Physics

hard

easy

hard

easy

medium