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Capacitor question

2011 · Q162
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Capacitor question

2011 · Q162

NEETPhysicsCapacitorMCQ+4 / −1
A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is
  1. A
    12ε0E2{1 \over 2}{\varepsilon _0}{E^2}21​ε0​E2
  2. B
    E2Adε0{{{E^2}Ad} \over {{\varepsilon _0}}}ε0​E2Ad​
  3. C
    12ε0E2Ad{1 \over 2}{\varepsilon _0}{E^2}Ad21​ε0​E2Ad
  4. D
    ε0EAd{\varepsilon _0}EAdε0​EAd
View written solutionFree

Correct answer: C

Capacitance of a parallel plate capacitor is

C=ε0AdC = {{{\varepsilon _0}A} \over d}C=dε0​A​   ...(i)

Potential difference between the plates is

V = Ed    ...(ii)

The energy stored in the capacitor is

U=12CV2=12(ε0Ad)(Ed)2U = {1 \over 2}C{V^2} = {1 \over 2}\left( {{{{\varepsilon _0}A} \over d}} \right){\left( {Ed} \right)^2}U=21​CV2=21​(dε0​A​)(Ed)2   (Using (i) and (ii))

=12ε0E2Ad = {1 \over 2}{\varepsilon _0}{E^2}Ad=21​ε0​E2Ad

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