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Physics · Electrostatic Potential

हिन्दी

A point charge \( Q \) is located at the origin. The work done by an external agent in slowly moving a test charge \( q \) from point \( r_1 \) to \( r_2 \) along a radial line (\( r_2 > r_1 \)) is proportional to:

  1. \( (r_2 - r_1) \)
  2. \( (\frac{1}{r_2} - \frac{1}{r_1}) \)
  3. \( (\frac{1}{r_1^2} - \frac{1}{r_2^2}) \)
  4. \( (\frac{1}{r_1} - \frac{1}{r_2}) \)

Correct answer · Option 4

\( (\frac{1}{r_1} - \frac{1}{r_2}) \)

Explanation

Work done \( W = -\int_{r_1}^{r_2} \frac{Qq}{4\pi\varepsilon_0 r^2} dr = \frac{Qq}{4\pi\varepsilon_0} (\frac{1}{r_1} - \frac{1}{r_2}) \).
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