Question #42793

A parallel plate capacitor has rectangular plates of length $L$, width $w$, and separation $d$. It is initially connected to a battery of constant voltage $V_0$ with air between the plates. The battery is then disconnected. A rigid dielectric slab of the same dimensions ($L \times w \times d$) is subsequently inserted between the plates from one end (along the length $L$). The dielectric constant of the slab varies along its length as $K(\xi) = 5 - \frac{4\xi}{L}$, where $\xi$ is the distance from the leading edge of the slab. When the slab has been inserted by a distance $x = L/2$, what is the magnitude of the electric force pulling the slab into the capacitor? (Assume ideal parallel plate behavior for capacitance calculations)