A cube of side b has a charge q at each of its vertices. Determine the potential and electric field due to this charge array at the centre of the cube.
Given, side of the cube = b units
Charge at each vertices = q C
In the cube shown above,
d = diagonal of any face = 
= 
b units
l = diagonal of whole cube = 
= √3 b units
Thus, distance of centre of the cube from each vertices = 
= 
units
∴ Electric potential at the centre of the cube, V = 
(∵ 8 charges)
Where,
q = charge
d = distance from origin
ϵ0 = permittivity of space
∴ V = 
N units C-1
Since, the electric charge uniformly distributed with respect to the centre of the cube the electric field at centre is ZERO.
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