Question 2 of 11intermediate🔧 ApplyNumerical2 marks

A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.

Correct Answer

2.7×102.7 \times 10⁹ V

Exercise: EXERCISES | Q: 2.2 | (Page 79)
For More Understanding

Explanation

This numerical problem tests understanding of electrostatic potential due to multiple point charges. The key insight is that in a regular hexagon, all vertices are equidistant from the centre, with the distance equal to the side length. Since potential is a scalar quantity, the total potential at the centre is simply the algebraic sum of potentials due to each charge. The formula V = (1/4πε₀) × q/r from Example 2.1 in the textbook is applied. With 6 identical charges at equal distances, we multiply the potential due to one charge by 6.

Solution Steps

  1. Given: Number of charges = 6; Charge at each vertex, q = 5 mC = 5×105 \times 10⁻³ C; Distance from centre to each vertex, r = 10 cm = 0.1 m

  2. Formula: Potential due to a point charge, V = (1/4πε₀) × q/r, where (1/4πε₀) = 9×109 \times 10⁹ Nm²/C²

  3. Calculation: Since all 6 charges are equidistant from the centre and potential is a scalar quantity, V_total = 6 × V_single = 6 × (1/4πε₀) × q/r

  4. Substitution: V_total = 6×96 \times 9 × 10⁹ × (5×105 \times 10⁻³)/(0.1) = 6×96 \times 9 × 10⁹ × 50×1050 \times 10⁻³ = 6×96 \times 9 × 50×1050 \times 10⁶ = 2700×102700 \times 10⁶

  5. Answer: V_total = 2.7×102.7 \times 10⁹ V

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