Review. A slab of insulating material (infinite in the y and z directions) has a thickness d and a uniform pos- itive charge density p. An edge view of the slab is shown in Figure P23.45. (a) Show that the magnitude of the electric field a dis- tance x from its center and inside the slab is E = px/e,. (b) What If? Suppose an electron of charge -e and mass m, can move freely within the slab. It is released from rest at a distance x from the center. Show that the elec- tron exhibits simple harmonic motion with a frequency 1 pe m Eo Figure P23.45 Problems 45 and 49.

с A slab of copper of thickness b is thrust into a parallel-plate capacitor of plate area A and plate separation d, as shown in the figure above; the slab is exactly halfway between the plates. NOTE: Express your answers in terms of the given variables using eo and q when necessary. (a) What is the capacitance after the slab is introduced? = W b (b) If a charge q is maintained on the plates, what is the ratio of the stored energy before to that after the slab is inserted? d U₁ Uf (c) How much work is done on the slab as it is inserted? = = (d) Is the slab sucked in or must it be pushed in? [Choose one ▾

The space a ≤ r ≤ c < b between cylindrical capacitors of length L, radius a,b and is filled with a dielectric constant K, and the remaining space is vacuum. The potential difference between the capacitor plates is V. (a) Find the electric capacitance. (b) Find the electric field E, electric displacement D, and polarization P in c < r < b

The battery below has a potential difference of 536 V. 4.00 cm B V 4.00 cm 4.00 cm D