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. $7.2\times {10}^{1}1V$
• C. $2.5\times {10}^{1}2V$
• D. $3.4\times {10}^{4}V$

Answer 1

The correct option is A $2.7\times {10}^{6}V$

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.
$\therefore OA=OB=OC=OD=OE=OF=8cm=8\times {10}^{-2}m$
The potential at O is
$V=6\times \frac{q}{4\pi {ϵ}_{0}r}=\frac{6\times 9\times {10}^9\times 4\times {10}^{-6}}{8\times {10}^{-2}}=2.7\times {10}^{6}V$