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Physics · Electrostatic Potential
हिन्दीThe electric field between two plates of a parallel plate capacitor is \( E \). If the separation between the plates is doubled and the space is completely filled with a medium of dielectric constant \( K = 3 \) while keeping the charge on the plates unchanged, the new electrostatic energy density in the region between the plates becomes:
Correct answer · Option A
\( \frac{1}{3} u_0 \)
Explanation
Initial energy density \( u_0 = \frac{1}{2} \varepsilon_0 E^2 = \frac{\sigma^2}{2\varepsilon_0} \). With constant \( Q \), charge density \( \sigma \) is constant. In the dielectric medium, new energy density is \( u = \frac{1}{2} \varepsilon E_{\text{new}}^2 = \frac{1}{2} (K \varepsilon_0) (\frac{E}{K})^2 = \frac{u_0}{K} = \frac{1}{3} u_0 \), independent of separation \( d \).
