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JEE Main202622 January 2026Evening ShiftPhysicsElectrostaticsActual

Five positive charges each having charge q are placed at the vertices of a pentagon as shown in the figure. The electric potential (V) and the electric field ( E ) at the center O of the pentagon due to these five positive charges are:

Options

  1. AV= 5 q 4 _ o r and E = 5 3 q 8 _ o r² r
  2. BV= 5 q 4 _ o r and E =0
  3. CV=0 and E =0
  4. DV= 5 q 4 _ o r and E = 5 q 4 _ o r² r

Correct answer

B. V= 5 q 4 _ o r and E =0

Step-by-step solution

The electric potential at center O is the scalar sum of contributions from all 5 charges. Each charge is equidistant from center, so V = 5 cdot kq r = 5q 4 ₀ r . The electric field is a vector sum of field vectors from all 5 charges. Due to 5-fold rotational symmetry of a regular pentagon, the 5 field vectors point radially outward from center, equally spaced at 72° angles. The vector sum of 5 equally spaced unit vectors is zero, so E = 0 .

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