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Q.
Equal charges $q$ each are placed at the vertices of an equilateral triangle of side $r$. The magnitude of electric field intensity at any vertex is
The magmitude of intensity of electric field at point
$C$ due to charge at $A$ and $B$ is
$ E_{1}=E_{2}=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q}{I^{2}}$
So, the net intensity at point $C$ is
$E_{R}=\sqrt{E_{1}^{2}+E_{2}^{2}+2 E_{1} E_{2} \cos 60^{\circ}}$
$=\sqrt{E_{1}^{2}+E_{1}^{2}+2 E_{1}^{2} \times \frac{1}{2}}=\sqrt{3}$
$\therefore E_{1}=\frac{\sqrt{3} q}{4 \pi \varepsilon_{0} r^{2}}$
