Question

In a parallel plate capacitor, the plate at $x = 0$ is grounded and the plate at $x = d$ is maintained at a potential $V_0$. The space between the two plates is filled with a linear dielectric of permittivity $\epsilon = \epsilon_0 \left(1 + \frac{x}{d}\right)$, where $\epsilon_0$ is the permittivity of free space. Neglecting the edge effects, the electric field ($\vec{E}$) inside the capacitor is .

• A. $-\frac{V_0}{(d+x)ln 2}\hat{x}$
• B. $-\frac{V_0}{d}\hat{x}$
• C. $-\frac{V_0}{(d+x)}\hat{x}$
• D. $-\frac{V_0d}{(d+x)x}\hat{x}$

Answer 1

Answer: (A)

$-\frac{V_0}{(d+x)ln 2}\hat{x}$

Answer 2

The correct option is (A) :$-\frac{V_0}{(d+x)ln 2}\hat{x}$