Consider a solid cube of uniform charge density of insulating material. What is the ratio of the electrostatic potential at a corner to that at the centre: (Take the potential to be zero at infinity, as usual) –
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ρ − Charge density of the cube
– Potential at the corner of a cube of side λ
– Potential at the centre of a cube of side λ
–
Potential at the center of a cube of side 
–
Potential at the corner of a cube of side 
By dimensional analysis
∝ 
= ρ λ 2 
= 4 
But by superposition 
= 
Because of the center of the larger cube lies at a corner of the eight smaller cubes of which it is made
Therefore, 
= 
= 
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