Equal charges q are placed at vertices A and B of an equilateral triangle ABC of side a . magnitude

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1. Electric Charges and Fields

medium

Equal charges $q$ are placed at the vertices $A$ and $B$ of an equilateral triangle $ABC$ of side $a$. The magnitude of electric field at the point $C$ is

$\frac{q}{{4\pi {\varepsilon _0}{a^2}}}$

$\frac{{\sqrt 2 \,q}}{{4\pi {\varepsilon _0}{a^2}}}$

$\frac{{\sqrt 3 \,q}}{{4\pi {\varepsilon _0}{a^2}}}$

$\frac{q}{{2\pi {\varepsilon _0}{a^2}}}$

Solution

(c) $|{E_A}|\, = \,|{E_B}| = k.\frac{q}{{{a^2}}}$
So, ${E_{net}} = \sqrt {E_A^2 + E_B^2 + 2{E_A}{E_B}\cos 6{0^o}} $
$ = \frac{{\sqrt 3 \,k.\,q}}{{{a^2}}}$
$==>$ ${E_{net}} = \frac{{\sqrt 3 \,q}}{{4\pi {\varepsilon _0}{a^2}}}$

Standard 12

Physics

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