Question

A hexagon of side $8 \,cm$ has a charge $4\,\mu\,C$ at each of its vertices. The potential at the centre of the hexagon is

• A. $2.7 \times 10^6\,V$
• B. $7.2 \times 10^{11}\, V$
• C. $2.5 \times 10^{12}\, V$
• D. $3.4 \times 10^4 \, V$

Answer 1

Answer: (A)

As shown in the figure, O is the centre of hexagon ABCDEF of each side 8 cm. As it is a regular hexagon OAB, OBC, etc are equilateral triangles.
∴ OA = OB = OC = OD = OE = OF = 8 cm
$\quad\quad$$\quad\quad\quad$= 8 × 10^-2 m
The potential at O is
$V=6\times\frac{q}{4\pi\varepsilon_{0}r}$
$\quad=\frac{6\times9\times10^{9}\times4\times10^{-6}}{8\times10^{-2}}=2.7\times10^{6} V$