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A parallel plate capacitor is filled with two layers of different materials A and B as shown in fig. The material A has dielectric constant $k_{1}$ and conductivity $σ_{1}$ and material B has dielectric constant $k_{2}$ and conductivity $σ_{2}$ . The capacitor is connected across an ideal battery of terminal voltage V. Permittivity of free space is $\in_{0}$ . Choose incorrect statement:

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The current in the two materials is different

The electric field in the material A is $\frac{V σ_{2}}{d_{1} σ_{2} + d_{2} σ_{1}}$

The total surface charge density on the interface of the two materials is $\frac{\in_{0} V (σ_{1} - σ_{2})}{d_{1} σ_{2} + d_{2} σ_{1}}$

The electric field in the material B is $\frac{V σ_{1}}{d_{1} σ_{2} + d_{2} σ_{1}}$

answer is D.

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Detailed Solution

$C u r r e n t = I = \frac{V}{R_{1} + R_{2}} J = \frac{I}{A} = σ_{1} E_{1} = σ_{2} E_{2}; c h \arg e q = (Δ ϕ) \in_{0} σ = s u r f a c e c h n g e d e n s i t y = (E_{1} - E_{2}) \in_{0}$

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