Question

Six identical charges \(+q\)are placed at the corners of a regular hexagon shown in the figure. The charge \(Q\), that should be placed at the centre of hexagon so that the net force on the charge placed at any corner is zero

B

• A. $Q=–2.17q$
• B. $Q=–0.79$
• C. $Q=–0.94q$
• D. $Q=–1.83q$

Answer 1

The correct option is D $Q=–1.83q$

${\overrightarrow{F}}_{net}=0$

Let $AB=r$, then $AC=\sqrt{3}r$ and $AD=2r$

$F_1=\frac{1}{4\pi {ϵ}_0}\frac{q^2}{r^2}$

$F_2=\frac{1}{4\pi {ϵ}_0}\frac{q^2}{[\sqrt{3}r{]}^2}$

​​​​​​​$F_3=\frac{1}{4\pi {ϵ}_0}\frac{q^2}{(2r{)}^2}$

​​​​​​​$F_4=\frac{1}{4\pi {ϵ}_0}\frac{Qq}{r^2}$

$F_1+\sqrt{3}{F}_2+F_3+F_4=0$

​​​​​​​$Q=-q\left(1.827\right)$