Question 826: Electrostats & Capacitance

Question

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

Accepted Answer

$$\begin{aligned}
&	ext { Potential at the centre of hexagon }\
&\begin{aligned}
& 	ext { Potential at } \
& V_0=V_A+V_B+V_C+V_D+V_E+V_F \
& \quad=\frac{1}{4 \pi \varepsilon_0}\left[\frac{q}{O A}+\frac{q}{O B}+\frac{q}{O C}+\frac{q}{O D}+\frac{q}{O E}+\frac{q}{O F}ight]
\end{aligned}
\end{aligned}$$
For a hexagon, distance from centre to vertices is equal to length of side.
$$\begin{aligned}
& 	herefore \quad \mathrm{OA}=\mathrm{OB}=\mathrm{OC}=\mathrm{OD}=\mathrm{OE}=\mathrm{OF}=10 \mathrm{~cm} \
& =0.1 \mathrm{~m} \
& 	herefore \quad \mathrm{~V}_0=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{q}}{0.1}(6) \
& =9 	imes 10^9 	imes \frac{\left(1 	imes 10^{-6}ight) 6}{0.1} \
& =5.4 	imes 10^5 	ext { volt }
\end{aligned}$$

Answer

$1.8 	imes 10^5$ volt

Answer

$3.6 	imes 10^5$ volt

Answer

$5.4 	imes 10^5$ volt

Answer

$7.2 	imes 10^5$ volt

Electrostats & Capacitance

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

Choose the correct answer: