MHT CET202523 Apr 2025Morning ShiftPhysicsElectrostaticsActual
A regular hexagon of side 6 cm has a charge of 2 C at each of its vertices, what is the potential at the centre of the hexagon? [ 1 4 ₀ =9 10^9 SI unit ]
Options
- A1.5 10^5 ~V
- B1.8 10^6 ~V
- C2.4 10^5 ~V
- D3.2 10^6 ~V
Correct answer
B. 1.8 10^6 ~V
Step-by-step solution
Potential at Center of Regular Hexagon The center of a regular hexagon is equidistant from all six vertices, each carrying charge q = 2 10⁻⁶ , C . With side length r = 0.06 , m , the distance from each vertex to the center is also r . The potential due to a single charge at the center is 1 4 ₀ q r , where 1 4 ₀ = 9 10^9 , N , m ^2/ C ^2 . By superposition, the total potential is six times this value: V_ total = 6 9 10^9 2 10⁻⁶ 0.06 Simplifying, V_ total = 108 10^9 10⁻⁶ 1 0.06 = 108 10^3 1 0.06 = 1.8 10^6 , V . This