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MHT CET202620 April 2026Evening ShiftPhysicsElectrostaticsActual

A charge Q is placed at each corner of a cube of side r . The potential at the centre of the cube is ( ₀ = permittivity of free space)

Options

  1. A4Q ₀ r 3
  2. B8Q ₀ r 3
  3. C16Q 3 ₀ r
  4. D32Q ₀ r 3

Correct answer

A. 4Q ₀ r 3

Step-by-step solution

The length of the body diagonal of a cube of side r is r 3 . The distance from the centre of the cube to any corner is half of the body diagonal, which is d = r 3 2 . The electric potential at the centre due to a single charge Q at one corner is V₁ = 1 4 ₀ Q d . Since there are 8 identical charges at the 8 corners, the total potential at the centre is V = 8 V₁ . Substituting the value of d : V = 8 1 4 ₀ Q r 3 2 V = 16Q 4 ₀ r 3 V = 4Q ₀ r 3 Answer: 4Q ₀ r 3

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