Question

A hexagon of side $8cm$ 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
= 8 × 10^-2 m
The potential at O is
$V=6\times \frac{q}{4\pi {\epsilon }_{0}r}$
$=\frac{6\times 9\times 10^9\times 4\times 10^{-6}}{8\times 10^{-2}}=2.7\times 10^{6}V$