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Question
A cube of side b hasa charge q at each of its vertices. Determine the potentialand electric field due to this charge array at the centre of thecube.
A cube of side b hasa charge q at each of its vertices. Determine the potentialand electric field due to this charge array at the centre of thecube.
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Solution
Length of the side of acube = b
Charge at each of itsvertices = q
A cube of side b isshown in the following figure.
d = Diagonal ofone of the six faces of the cube
l = Length ofthe diagonal of the cube
The electric potential(V) at the centre of the cube is due to the presence of eightcharges at the vertices.
Therefore, thepotential at the centre of the cube is 
.
The electric field atthe centre of the cube, due to the eight charges, gets cancelled.This is because the charges are distributed symmetrically withrespect to the centre of the cube. Hence, the electric field is zeroat the centre.
Length of the side of acube = b
Charge at each of itsvertices = q
A cube of side b isshown in the following figure.
d = Diagonal ofone of the six faces of the cube
l = Length ofthe diagonal of the cube
The electric potential(V) at the centre of the cube is due to the presence of eightcharges at the vertices.
Therefore, thepotential at the centre of the cube is .
The electric field atthe centre of the cube, due to the eight charges, gets cancelled.This is because the charges are distributed symmetrically withrespect to the centre of the cube. Hence, the electric field is zeroat the centre.
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