Q. 133.6( 15 Votes )

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.

Answer :

Given, side of the cube = b units

Charge at each vertex = q C

In the cube shown above,

d = diagonal of any face = = b units

l = diagonal of whole cube = = √3 b units

Thus, the distance of centre of the cube from each vertices = = units

Electric potential at the centre of the cube, V =

( 8 charges)


q = charge

d = distance from origin=

ϵ0 = permittivity of space

V = N units C-1

As the charges as symmetrically placed along the vertex of the cube, the net Electric field will be zero at the centre as the field due to 2 charges placed opposite to each other will cancel, so for all charges, net field will be 0. 

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