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Help me answer: - Electrostatics - JEE Main-12

 The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose permittivity varies linearly from \epsilon_{1} at one plate to \epsilon _{2} at the other. The capacitance of capacitor is :    

 

  • Option 1)

    \epsilon _{0}\left ( \epsilon _{1} +\epsilon _{2}\right )A/d

  • Option 2)

    \epsilon _{0}\left ( \epsilon _{2} +\epsilon _{1}\right )A/2d

  • Option 3)

    \epsilon _{0}A/\left [ d\: ln\left ( \epsilon _{2}/\epsilon _{1} \right ) \right ]

  • Option 4)

    \epsilon _{0}\left ( \epsilon _{2} - \epsilon _{1}\right )A/\left [ d\: ln\left ( \epsilon _{2}/\epsilon _{1} \right ) \right ]

 
Answers (2)
89 Views
N neha
S solutionqc

As we discussed in

If K filled between the plates -

{C}'=K\frac{\epsilon _{0}A}{d}={C}'=Ck

 

 

- wherein

C\propto A

C\propto\frac{1}{d}

 

 

 

dV=\frac{E_0}{k}dx\\V=\int_{0}^{d}\frac{\sigma dx}{\varepsilon _0\frac{(\varepsilon _2-\varepsilon _1)}{d}x+\varepsilon _1}\\V=\frac{\varepsilon d}{\varepsilon _0(\varepsilon _2-\varepsilon _1)}ln\frac{\varepsilon _2}{\varepsilon _1}\\Q=CV\\ \epsilon _{0}\left ( \epsilon _{2} - \epsilon _{1}\right )A/\left [ d\: ln\left ( \epsilon _{2}/\epsilon _{1} \right ) \right ]


Option 1)

\epsilon _{0}\left ( \epsilon _{1} +\epsilon _{2}\right )A/d

Option 2)

\epsilon _{0}\left ( \epsilon _{2} +\epsilon _{1}\right )A/2d

Option 3)

\epsilon _{0}A/\left [ d\: ln\left ( \epsilon _{2}/\epsilon _{1} \right ) \right ]

Option 4)

\epsilon _{0}\left ( \epsilon _{2} - \epsilon _{1}\right )A/\left [ d\: ln\left ( \epsilon _{2}/\epsilon _{1} \right ) \right ]

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