Three charges each of $+1 \mu \mathrm{C}$ are placed at the corners of an equilateral triangle. If the…

Three charges each of $+1 \mu \mathrm{C}$ are placed at the corners of an equilateral triangle. If the repulsive force between any two charges is $\mathrm{F}$, then the net force on either charge will be
  1. $2 \mathrm{~F}$
  2. $3 \mathrm{~F}$
  3. $\sqrt{2} \mathrm{~F}$
  4. $\sqrt{3} \mathrm{~F}$

Solution

The force on any charge due to each of the other two charges has magnitude $\mathrm{F}$. The angle between the two forces is $60^{\circ}$. Hence the resultant force is given by $R=\sqrt{F^2+F^2+2 F^2 \cos 60^{\circ}}=\sqrt{3} F$

Asked in: MHT CET 2021 (24 Sep Shift 2)

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