Question : A regular hexagon of side 10 cm has a charge 5µC at each of its vertices. Calculate the potential at the centre of the hexagon.
Doubt by Dev.
Solution :
We know, a hexagon has six vertices so there will be 6 charges and each having a charge of 5µC.
q = 5µC
q = 5×10-6 C
Each side of regular hexagon (a)
= 10 cm
= 10×10-2 m
We know, In regular hexagon - the internal angle is 120°. So by using geometry. We can say that distance of each vertex from the centre must be equal to the side of the regular hexagon.
Hence
r = a = 10×10-2 m
Now,
Electric Potential at the centre due to each charge q will be given by
= kq/r
Hence, Total Electric Potential at the centre due to all 6 charges at the vertices will be
V = (6×kq)/r
= (6×9×109×5×10-6 C)/10×10-2 m
= (270×103)/10-1
= 270×104
= 2.7×106 V
Hence, the total potential at the centre of the hexagon will be 2.7×106 V
