Three infinitely long linear charges of charge density , and -2 a… - Vidyadip

MCQ

Three infinitely long linear charges of charge density $\lambda $ , $\lambda $ and $-2\lambda $ are placed in space. A point in space is specified by its perpendicular distance $r_1 , r_2 $ and $ r_3$ respectively from the linear charges. For the points which are equipotential

✓
$\frac{{{r_1}{r_2}}}{{r_3^2}} = $ constant
B
${r_1}{r_2}{r_3}^2 = $ constant
C
${r_1}{r_2}{r_3}^{1/2} = $ constant
D
${r_1}{r_2}{r_3} = $ constant

✓

Answer

Correct option: A.

$\frac{{{r_1}{r_2}}}{{r_3^2}} = $ constant

a
$2{\rm{k}}\lambda \ln \left( {\frac{{\rm{a}}}{{{{\rm{r}}_1}}}} \right) + 2{\rm{k}}\lambda \ln \left( {\frac{{\rm{a}}}{{{{\rm{r}}_2}}}} \right) + 4{\rm{k}}\lambda \ln \left( {\frac{{\rm{a}}}{{{{\rm{r}}_3}}}} \right) = {\rm{c}}$

$=\frac{\mathrm{r}_{3}^{2}}{\mathrm{r}_{1} \mathrm{r}_{2}}=$ const.

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