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Question: Answered & Verified by Expert
A hexagon of side $8 \mathrm{~cm}$ has a charge $4 \mu \mathrm{C}$ at each of its vertices. The potential at the centre of the hexagon is
PhysicsElectrostaticsAIIMSAIIMS 2015
Options:
  • A $2.7 \times 10^6 \mathrm{~V}$
  • B $7.2 \times 10^{11} \mathrm{~V}$
  • C $2.5 \times 10^{12} \mathrm{~V}$
  • D $3.4 \times 10^4 \mathrm{~V}$
Solution:
1969 Upvotes Verified Answer
The correct answer is: $2.7 \times 10^6 \mathrm{~V}$




As shown in the figure, $O$ is the centre of hexagon $A B C D E F$ of each side $8 \mathrm{~cm}$. As it is a regular hexagon $O A B, O B C$, etc are equilateral triangles.
$$
\begin{aligned}
\therefore \quad O A=O B=O C= & O D=O E=O F=8 \mathrm{~cm} \\
& =8 \times 10^{-2} \mathrm{~m}
\end{aligned}
$$
The potential at $O$ is
$$
\begin{aligned}
V & =6 \times \frac{q}{4 \pi \varepsilon_0 r} \\
& =\frac{6 \times 9 \times 10^9 \times 4 \times 10^{-6}}{8 \times 10^{-2}}=2.7 \times 10^6 \mathrm{~V}
\end{aligned}
$$

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