A parallel plate capacitor having a plate separation of \(2 \mathrm{~mm}\) is charged by connecting it to a…

A parallel plate capacitor having a plate separation of \(2 \mathrm{~mm}\) is charged by connecting it to a \(300 \mathrm{~V}\) supply. The energy density is
  1. \(0.01 \mathrm{~J} / \mathrm{m}^{3}\)
  2. \(0.1 \mathrm{~J} / \mathrm{m}^{3}\)
  3. \(1.0 \mathrm{~J} / \mathrm{m}^{3}\)
  4. \(10 \mathrm{~J} / \mathrm{m}^{3}\)

Solution

The energy density of parallel plate capacitor given by \(U=\frac{1}{2} \varepsilon_{0} E^{2}=\frac{1}{2} \varepsilon_{0}\left(\frac{V}{d}\right)^{2}\)
\(=\frac{1}{2} \times 8.85 \times 10^{-12} C^{2} / N m^{2} \times\left(\frac{300 v o l t}{2 \times 10^{-3} m}\right)\)
\(=0.1 \mathrm{~J} / \mathrm{m}^{3}\) *

Asked in: JEE Mains - Capacitance - Chapter Test

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