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Physics · Electrostatic Potential

English

कुल आवेश \( q \) और त्रिज्या \( R \) के एक समान रूप से आवेशित पतले गोलीय खोल (शेल) का \( r \) दूरी (\( r < R \)) पर स्थित किसी आंतरिक बिंदु पर विद्युत विभव होता है:

  1. A
    \( \frac{1}{4\pi\varepsilon_0} \frac{q}{R} \)
  2. B
    \( \frac{1}{4\pi\varepsilon_0} \frac{q}{r} \)
  3. C
    शून्य
  4. D
    \( \frac{1}{4\pi\varepsilon_0} \frac{q r}{R^2} \)
उत्तर और समाधान देखें

सही उत्तर · विकल्प A

\( \frac{1}{4\pi\varepsilon_0} \frac{q}{R} \)

व्याख्या

For a uniformly charged thin spherical shell of radius \( R \) and total charge \( q \), the electric field inside the shell (\( r < R \)) is zero (\( E = 0 \)). Since the electric field is related to the electric potential by \( E = -\frac{dV}{dr} \), a zero electric field means that the electric potential remains constant throughout the interior region and is equal to its value at the surface. Therefore, the electric potential at any internal point where \( r < R \) is given by \( V = \frac{1}{4\pi\varepsilon_0} \frac{q}{R} \).
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