A ring of radius R is charged uniformly with a charge +,Q . electric field at a point on its axis at

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1. Electric Charges and Fields

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A ring of radius $R$ is charged uniformly with a charge $+\,Q$ . The electric field at a point on its axis at a distance $r$ from any point on the ring will be

A

$\frac{{KQ}}{{({r^2} - {R^2})}}$

B

$\frac{{KQ}}{{{r^2}}}$

C

$\frac{{KQ}}{{{r^3}}}{({r^2} - {R^2})^{1/2}}$

D

$\frac{{KQr}}{{{R^3}}}$

Solution

$ \mathrm{E}=\frac{\mathrm{k} \mathrm{Q} \mathrm{x}}{\left(\mathrm{R}^{2}+\mathrm{x}^{2}\right)^{3 / 2}} $

$ \mathrm{r}^{2}= \mathrm{R}^{2}+\mathrm{x}^{2} $

$ \mathrm{x}^{2}=\mathrm{r}^{2}-\mathrm{R}^{2} $

Standard 12

Physics

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