Question 773: Electrostats & Capacitance

Question

A regular hexagon of side 6 cm has a charge of $2 \mu \mathrm{C}$ at each of its vertices, what is the potential at the centre of the hexagon?
$$ \left[\frac{1}{4 \pi \varepsilon_0}=9 	imes 10^9 	ext { SI unit }ight] $$

Accepted Answer

Potential at the centre of hexagon
$$ \begin{aligned} V_0 & =V_A+V_B+V_C+V_D+V_E+V_F \ & =\frac{1}{4 \pi \varepsilon_0}\left[\frac{q}{O A}+\frac{q}{O B}+\frac{q}{O C}+\frac{q}{O D}+\frac{q}{O E}+\frac{q}{O F}ight] \end{aligned} $$
For a hexagon, distance from centre to vertices is equal to length of side.
$$ \begin{aligned} 	herefore \quad \mathrm{OA} & =\mathrm{OB}=\mathrm{OC}=\mathrm{OD}=\mathrm{OE}=\mathrm{OF}=6 \mathrm{~cm}  =6 	imes 10^{-2} \mathrm{~m} \ 	herefore \quad \mathrm{~V}_0 & =\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{q}}{6 	imes 10^{-2}}(6) \ & =9 	imes 10^9 	imes \frac{\left(2 	imes 10^{-6}ight) 6}{6 	imes 10^{-2}} \ & =1.8 	imes 10^6 \mathrm{~V} \end{aligned} $$

Answer

$1.5 	imes 10^5 \mathrm{~V}$

Answer

$1.8 	imes 10^6 \mathrm{~V}$

Answer

$2.4 	imes 10^5 \mathrm{~V}$

Answer

$3.2 	imes 10^6 \mathrm{~V}$

Electrostats & Capacitance

A regular hexagon of side 6 cm has a charge of 2 \mu \mathrm{C} at each of its vertices, what is the potential at the centre of the hexagon? $ \left[\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text { SI unit }\right]

Choose the correct answer: