Question

Three identical charges are placed at the comers of an equilateral triangle. If the force between any two charges is F, then the net force on each will be

• A. $\sqrt{2}$ F
• B. 2 F
• C. $\sqrt{2}$ F
• D. 3 F

Answer 1

Answer: (C)

Net force on each charge will be $F_{net}=\sqrt{F^2+F^2+2F^2\cos 60{}^{\circ }}$ $\Rightarrow$ $F_{net}=\sqrt{2F^2+2F^2\times \frac{1}{2}}$ $\Rightarrow$ $F_{net}=\sqrt{2F^2+F^2}$ $\Rightarrow$ $F_{net}=\sqrt{3F^2}$ $\therefore$ $F_{net}=\sqrt{3}F$