Question

A parallel plate capacitor has two layers of dielectric as shown in figure. This capacitor is connected across a battery. The graph which shows the variation of electric field (E) and distance (x) from left plate :

• A. Graph (1)
• B. Graph (2)
• C. Graph (3)
• D. Graph (4)

Answer 1

Answer: (A)

1

Answer 2

The electric displacement vector $D = k \epsilon_0 E$ is constant across the series dielectric layers in a parallel plate capacitor connected to a battery. Therefore, $k_1 E_1 = k_2 E_2$. Given $k_1=2$ and $k_2=4$, we get $2 E_1 = 4 E_2$, which simplifies to $E_1 = 2 E_2$. This means the electric field in the first layer (where $k=2$) is twice the electric field in the second layer (where $k=4$). Also, the electric field is constant within each uniform dielectric layer. Graph (1) shows a constant higher electric field for $0 \le x \le d$ and a constant lower electric field for $d < x \le 3d$, consistent with $E_1 = 2 E_2$.