Question

A point charge $+Q$ is placed at the centroid of an equilateral triangle. When second charge $+Q$ is placed at the vertex of the triangle the magnitude of the electrostatic force on the central charge is $8N.$ The magnitude of the net force on the central charge when a third charge $+Q$ is placed at another vertex of the triangle is

• A. Zero
• B. $4N$
• C. $4\sqrt{2}N$
• D. $8N$

Answer 1

Answer: (D)

$8N$

Given, ${\overrightarrow{F}}_{OA}:$ {Force on central charge due to charge at vertex $A$ is given by} $=8N$

Similarly due to symmetry, ${\overrightarrow{F}}_{OB}=8N$

$\therefore$ There are 2 resultant force acting on, ${\overrightarrow{F}}_{OA}\&{\overrightarrow{F}}_{OB}$ and the angle between them is given by ${120}^0$.

$\therefore$ Using parallelogram law of vector addition :-

${\overrightarrow{F}}_r=\sqrt{{\left({\overrightarrow{F}}_{OA}\right)}^2+{\left({\overrightarrow{F}}_{OB}\right)}^2+2F_{OA}{F}_{OB}cos{120}^0}$

$=\sqrt{8^2+8^2-8^2}\Rightarrow 8N$

$\therefore$ Option (D) is the correct option.