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Grade: 12th pass
        
The ratio of electrostatic potential at the centre of the cube to that at one of the corners of cube is
2 years ago

Answers : (1)

Arun
23742 Points
							The charge density within the cube is ,say, d. Then, to find the potential at any point of the cube we have to solve the Poission’s equation ( Laplacian operator)V=-d/(epsilon zero). In the absence of boundary conditions it would be impossible to find the solutions of above mentioned Poissions equation.
If we don't want to solve Poissions equation then we have to evaluate the following volume integral over the volume of the cube.
V(r)=(1/4 pi eo) integral[d/(|r-r’|) (d tau), where eo is permittivity of space and d tau is volume element.
But, if the cube is conductor, all the charge will reside on the surface and field inside the cube will be zero. In this case , potential at the corner and at center will be same and the ratio asked for is 1.

Regards
Arun (askIITians forum expert)
2 years ago
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