Q103 / 180 · AIIMS 2018 (27 May) · Physics

Electric field inside the given capacitor with dielectric is $E$ and dielectric constant of material is $K$. Find charge density $\sigma$ on the plates. (Given $E=6 \times 10^5 \mathrm{~V} / \mathrm{m}, K=6$ ) Figure

  • A
    $18.3 \times 10^{-6} \mathrm{C} / \mathrm{m}^2$
  • B
    $8.1 \times 10^{-7} \mathrm{C} / \mathrm{m}^2$
  • Correct answer
    C
    $3.18 \times 10^{-5} \mathrm{C} / \mathrm{m}^2$
  • D
    $3.18 \times 10^{-10} \mathrm{C} / \mathrm{m}^2$

Solution

$\begin{aligned} & \text {}: E=\frac{\sigma}{\varepsilon_0 \cdot K} ; 6 \times 10^5=\frac{\sigma}{8.85 \times 10^{-12} \times 6} \\ & \sigma=36 \times 8.85 \times 10^{-12} \times 10^5 \mathrm{C} / \mathrm{m}^2 \\ & \sigma=3.18 \times 10^{-5} \mathrm{C} / \mathrm{m}^2\end{aligned}$

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

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