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NEET 2011
Exam
NEET
Year
2011
Subject
Physics
Chapter
Capacitance

NEET 2011 · Physics · Capacitance

A parallel plate condenser has a uniform electric field E(~V / m)...

A parallel plate condenser has a uniform electric field E( V/m)E(\mathrm{~V} / \mathrm{m}) in the space between the plates. If the distance between the plates is d( m)andareaofeachplateisd(\mathrm{~m}) and area of each plate isA( m2)A\left(\mathrm{~m}^2\right) the energy (joule) stored in the condenser is

Options

  1. A12ε0E2\frac{1}{2} \varepsilon_0 E^2
  2. Bε0EAd\varepsilon_0 E A d
  3. C12ε0E2Ad\frac{1}{2} \varepsilon_0 E^2 A d
  4. DE2Ad/ε0E^2 A d / \varepsilon_0

Correct answer

C. 12ε0E2Ad\frac{1}{2} \varepsilon_0 E^2 A d

Step-by-step solution

The energy stored in the condenser U=12CV2U=12(Aε0d)(Ed)2(∵C=Aε0d and  V=Ed)U=12ε0E2Ad\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{\text{ and } } V=E d\right) \\ & U=\frac{1}{2} \varepsilon_0 E^2 A d \end{aligned}
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