CUET Preparation Today
Three charges q, -q, q placed at the vertices of an equilateral triangle as shown in figure. What is the magnitude of force on charge placed at position 3 due to the presence of other two charges?
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$\frac{1}{2 \pi \varepsilon_{o}} \frac{q^2}{l}$ $\frac{\sqrt{3}}{4 \pi \varepsilon_{o}} \frac{q^2}{l^2}$ $\frac{\sqrt{5}}{8 \pi \varepsilon_{o}} \frac{q}{\sqrt{l}}$ $\frac{1}{4 \pi \varepsilon_{o}} \frac{q^2}{\sqrt{l}}$ |
$\frac{\sqrt{3}}{4 \pi \varepsilon_{o}} \frac{q^2}{l^2}$ |
The correct answer is Option (2) → $\frac{\sqrt{3}}{4 \pi \varepsilon_{o}} \frac{q^2}{l^2}$ According to Coloumb's law, $F=K\frac{|q_1q_2|}{r^2}$ $F_{13}=K\frac{q^2}{l^2},F_{23}=K\frac{q^2}{l^2}$ $F_{net}=\sqrt{(F_{13x}+F_{23x})^2+(F_{13y}+F_{23y})^2}$ $=2F_{13x}=2F_{13}\cos(30°)$ $=K\frac{q^2}{l^2}\sqrt{3}$ |
