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Consider a solid cube made up of insulating material having a uniform volume charge density. Assuming the electrostatic potential to be zero at infinity, the ratio of the potential at a corner of the cube to that at the centre will be

Options

  1. A1 : 1
  2. B1 : 2
  3. C1 : 4
  4. D1 : 8

Correct answer

B. 1 : 2

Step-by-step solution

ρ - Charge density of the cube V l c o r n e r - Potential at the corner of a cube of side l V l c e n t r e - Potential at the centre of a cube of side l V l / 2 c e n t r e - Potential at the center of a cube of side l 2 V l / 2 c o r n e r - Potential at the corner of a cube of side l 2 By dimensional analysis V l c o r n e r ∝ Q l = ρ l 2 V l c o r n e r = 4 V l / 2 c o r n e r But by superposition V l c e n t r e = 8 V l / 2 c o r n e r Because of the centre of the larger cube lies at a corner of the eight sma

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