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Standard XII
Physics
Dielectrics and Polarisation
Question

A parallel plate capacitor is filled with two layers of different materials A and B as shown in the figure. The material A has dielectric constant $$k_1$$ and conductivity $$\sigma_1$$ and the material B has dielectric constant $$k_2$$ and conductivity $$\sigma_2$$. The capacity is connected across an ideal battery of terminal voltage V. Permitiviy of free space is $$\varepsilon_0$$.
What is the total surface charge density on the interface of the two materials?

A
$$\dfrac{\varepsilon_0V(k_1-k_2)}{d_1k_2+d_2k_1}$$
B
$$\dfrac{\varepsilon_0V(\sigma_1-\sigma_2)}{d_1\sigma_2+d_2\sigma_1}$$
C
$$\dfrac{V}{\varepsilon_0d_1d_2}\left[\dfrac{d_1}{d_1+d_2}-\dfrac{d_2}{d_1+d_2}\right]$$
D
$$\dfrac{\varepsilon_0V(\sigma_1k_2-\sigma_2k_1)}{d_1\sigma_2+d_2\sigma_1}$$
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Solution
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Correct option is B. $$\dfrac{\varepsilon_0V(\sigma_1-\sigma_2)}{d_1\sigma_2+d_2\sigma_1}$$

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