Q118 / 200 · NEET 2011 (Screening) · Physics

A parallel plate condenser has a uniform electric field $E(\mathrm{~V} / \mathrm{m})$ in the space between the plates. If the distance between the plates is $d(\mathrm{~m})$ and area of each plate is $A\left(\mathrm{~m}^2\right)$ the energy (joule) stored in the condenser is

  • A
    $\frac{1}{2} \varepsilon_0 E^2$
  • B
    $\varepsilon_0 E A d$
  • Correct answer
    C
    $\frac{1}{2} \varepsilon_0 E^2 A d$
  • D
    $E^2 A d / \varepsilon_0$

Solution

The energy stored in the condenser $\begin{aligned} & U=\frac{1}{2} C V^2 \\ & U=\frac{1}{2}\left(\frac{A \varepsilon_0}{d}\right)(E d)^2 \quad\left(\because C=\frac{A \varepsilon_0}{d} \text { and } V=E d\right) \\ & U=\frac{1}{2} \varepsilon_0 E^2 A d \end{aligned}$

Hence, the correct answer is option: 'C'.

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