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Physics · JEE | Electric Charges and Fields

हिन्दी

Three charges \( +q, +q \) and \( -q \) are placed at the vertices of an equilateral triangle of side \( l \). The magnitude of the resultant electrostatic force on any one of the charges is:

  1. A
    \( \frac{1}{4\pi\varepsilon_0} \frac{q^2}{l^2} \)
  2. B
    \( \frac{\sqrt{2}}{4\pi\varepsilon_0} \frac{q^2}{l^2} \)
  3. C
    \( \frac{\sqrt{3}}{4\pi\varepsilon_0} \frac{q^2}{l^2} \)
  4. D
    \( \frac{2}{4\pi\varepsilon_0} \frac{q^2}{l^2} \)
View Answer & Solution

Correct answer · Option C

\( \frac{\sqrt{3}}{4\pi\varepsilon_0} \frac{q^2}{l^2} \)

Explanation

The force on a charge due to the other two charges each of magnitude \( q \) at distance \( l \) makes an angle of \( 60^\circ \) with each other. The resultant force is \( F_{\text{net}} = \sqrt{F^2 + F^2 + 2FF\cos(60^\circ)} = \sqrt{3}F = \frac{\sqrt{3}}{4\pi\varepsilon_0}\frac{q^2}{l^2} \).
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