Consider the potential at the corner of a uniformly charged cube of dimension L to be directly proportional to ρ L 2 L^2 L 2 , where ρ is volume charge density. The value of the ratio of the potential at the centre to the potential at the corner of the cube is n:1. Find n?
Physics · Electrostatic
JEE Mains Advanced

Question

Consider the potential at the corner of a uniformly charged cube of dimension L to be directly proportional to ρ L 2 L^2 L 2 , where ρ is volume charge density. The value of the ratio of the potential at the centre to the potential at the corner of the cube is n:1. Find n?

Physics · Electrostatic

G1 Physics · Accepted Answer

Step 1: Convert the density to charge using dq = ρ dV, dq = λ dl, or dq = σ dA as appropriate. Step 2: Integrate over the stated region and then use Coulomb's law/Gauss's law for the field or flux. Step 3: Apply the given radius/position limits and simplify. Final: 2. In this specific setup, apply the calculation to: Consider the potential at the corner of a uniformly charged cube of dimension L to be directly proportion.