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The electric charges ' +2 q', ' +2 q', ' -2 q' and ' -2 q' are placed at the corners of square of side ' 2 L ' as shown in figure. The electric potential at point ' A ', midway between the two charges ' +2 q ' and ' +2 q ' is ( ₀= permittivity of free space)

Options

  1. A1 4 ₀ ( 2 q L ) [1+ 1 5 ]
  2. Bq ₀ ~L [1- 1 5 ]
  3. Cq ₀ ~L [1+ 1 5 ]
  4. D1 4 ₀ ( 2 q L ) [1- 1 5 ]

Correct answer

B. q ₀ ~L [1- 1 5 ]

Step-by-step solution

The potential at point A is the sum of contributions from each point charge using V = 1 4 ₀ q r . Charges at (0, 0) and (0, 2L) , both +2q , are at distance L from A, contributing 1 4 ₀ 2q L each. Charges at (2L, 0) and (2L, 2L) , both -2q , are at distance (2L)^2 + L^2 = L 5 , contributing 1 4 ₀ -2q L 5 each. Summing all contributions yields: V_A = 1 4 ₀ ( 4q L - 4q L 5 ) = q ₀ L (1 - 1 5 ) This corresponds to option B .

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