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Capacitor question

2021 · 25 Jul · Shift 1 · Q52
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  5. /2021 · 25 Jul · Shift 1 · Q52

Capacitor question

2021 · 25 Jul · Shift 1 · Q52

JEE MainPhysicsCapacitorMCQ+4 / −1
A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as : ε(x)=ε0+kx\varepsilon (x) = {\varepsilon _0} + kxε(x)=ε0​+kx, for (0<x≤d2)\left( {0 \lt x \le {d \over 2}} \right)(0<x≤2d​)ε(x)=ε0+k(d−x)\varepsilon (x) = {\varepsilon _0} + k(d - x)ε(x)=ε0​+k(d−x), for (d2≤x≤d)\left( {{d \over 2} \le x \le d} \right)(2d​≤x≤d)
  1. A
    (ε0+kd2)2/kA{\left( {{\varepsilon _0} + {{kd} \over 2}} \right)^{2/kA}}(ε0​+2kd​)2/kA
  2. B
    kA2ln⁡(2ε0+kd2ε0){{kA} \over {2\ln \left( {{{2{\varepsilon _0} + kd} \over {2{\varepsilon _0}}}} \right)}}2ln(2ε0​2ε0​+kd​)kA​
  3. C
    0
  4. D
    kA2ln⁡(2ε02ε0−kd){{kA} \over 2}\ln \left( {{{2{\varepsilon _0}} \over {2{\varepsilon _0} - kd}}} \right)2kA​ln(2ε0​−kd2ε0​​)
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