A parallel-plate capacitor consists of square plates of edge length ℓ that are separated by a distance d, where d<<ℓ. A potential difference ΔV is maintained between the plates. A material of dielectric constant κ fills half the space between the plates. The dielectric slab is withdrawn from the capacitor as shown in the figure. (a) Find the capacitance when the left edge of the dielectric is at a distance x from the center of the capacitor. (Use the following as necessary: ℓ, ε0, κ, x, and d.) (b) If the dielectric is removed at a constant speed v, what is the magnitude of the current in the circuit, and its direction, as the dielectric is being withdrawn? (Use the following as necessary: ℓ, ε0, κ, ΔV, v, and d.)

A certain substance has a dielectric constant of 3.8 and a dielectric strength of 25 MV/m. If it is used as the dielectric material in a parallel-plate capacitor, what minimum area should the plates of the capacitor have to obtain a capacitance of 5.3 × 10-2 µ F and to ensure that the capacitor will be able to withstand a potential difference of 3.1 kV?

A parallel-plate capacitor has plates of area 0.11 m2 and a separation of 1.1 cm. A battery charges the plates to a potential difference of 130 V and is then disconnected. A dielectric slab of thickness 3.7 mm and dielectric constant 9.0 is then placed symmetrically between the plates. (a) What is the capacitance before the slab is inserted? (b) What is the capacitance with the slab in place? What is the free charge q (c) before and (d) after the slab is inserted? What is the magnitude of the electric field (e) in the space between the plates and dielectric and (f) in the dielectric itself? (g) With the slab in place, what is the potential difference across the plates? (h) How much external work is involved in inserting the slab? (a) Number i Units (b) Number i Units (c) Number i Units (d) Number Units (e) Number Units (f) Number Units

A cylindrical capacitor is made of two thin-walled concentric cylinders. The inner cylinder has radius R₂ = 7.5 mm, and the outer one a radius R = 14 mm. The region between the cylinders contains a dielectric with constant =3.6. The common length of the cylinders is L=7.5 m (Assume the cylinders can be treated as ideal infinite cylinders.) Determine the potential energy stored in this capacitor when a potential difference V = 38.8V is applied between the inner and outer cylinders in n.J. ME hp