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Physics · Electrostatic Potential

हिन्दी

Four charges are arranged at the corners of a square ABCD of side \( d \), with \( +q \) at A and C, and \( -q \) at B and D. The total electrostatic potential energy of this configuration is:

  1. \( -\frac{q^2}{4\pi\varepsilon_0 d} ( 4 - \frac{1}{\sqrt{2}} ) \) / \( -\frac{q^2}{4\pi\varepsilon_0 d} ( 4 - \frac{1}{\sqrt{2}} ) \)
  2. \( -\frac{q^2}{4\pi\varepsilon_0 d} ( 2 - \frac{1}{\sqrt{2}} ) \) / \( -\frac{q^2}{4\pi\varepsilon_0 d} ( 2 - \frac{1}{\sqrt{2}} ) \)
  3. \( \frac{q^2}{4\pi\varepsilon_0 d} ( 4 + \frac{1}{\sqrt{2}} ) \) / \( \frac{q^2}{4\pi\varepsilon_0 d} ( 4 + \frac{1}{\sqrt{2}} ) \)
  4. \( -\frac{q^2}{4\pi\varepsilon_0 d} ( 2 + \frac{1}{\sqrt{2}} ) \) / \( -\frac{q^2}{4\pi\varepsilon_0 d} ( 2 + \frac{1}{\sqrt{2}} ) \)

Correct answer · Option 1

\( -\frac{q^2}{4\pi\varepsilon_0 d} ( 4 - \frac{1}{\sqrt{2}} ) \) / \( -\frac{q^2}{4\pi\varepsilon_0 d} ( 4 - \frac{1}{\sqrt{2}} ) \)

Explanation

Summing pairwise interactions for 4 corners (4 sides with distance \( d \) and 2 diagonals with distance \( \sqrt{2}d \)) yields \( -\frac{q^2}{4\pi\varepsilon_0 d} ( 4 - \frac{1}{\sqrt{2}} ) \).
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