Chapter 24, Problem 77E

(a)

To determine

The capacitance of the system.

(b)

To determine

To show: The change in stored energy $\left(dU\right)$ is $\frac{\left(K-1\right){\epsilon }_0{V}^{2}L}{2D}dx$.

(c)

To determine

The magnitude of the charge on each plate, and show that the energy changes by an amount of $-\frac{\left(K-1\right){\epsilon }_0{V}^{2}L}{2D}dx$ when $dx$ moves farther into the space between the plates.

(d)

To determine

To show: The pat (b) suggests that the electric force on the slab pushes out of the capacitor and the part (c) suggests that the force pulls the slab into the capacitor.

(e)

To determine

To explain: The reason for the electric force on the slab pulls into the capacitor for part (b) and to find the magnitude of the force.