A spherical capacitor consists of a spherical conducting shell of radius b and charge − Q concentric with a smaller conducting sphere of radius a and charge Q. (a) Find the capacitance of this device. (b) Show that as the radiusb of the outer sphere approaches infinity, the capacitance approaches the value  a/ ke = 4πϵ0a.

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) Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in the figure above. Take C1 = 2.00 µF, C2 = 14.0 µF, and C3 = 6.00 µF.(b) What charge is stored on C3 if the potential difference between points a and b is 60.0 V?

A parallel plate capacitor with a capacitance of 0.86 F with a has plate area A and are separated by a distance d. It is charged up to 11 V. The capacitor is now disconnected from the battery. If the area of the plates increases by a factor of 3 and the separation decreases by a factor of 10, find the new charge on the capacitor in Coulombs.

A certain capacitor has a capacitance of 4μF when its plates are separated by 0.2 mm of vacant space. A battery is used to charge the plate to a potential difference of 500 V and is then disconnected from the system. (a) What will be the potential difference across the plates if a sheet of mica 0.2 mm thick is inserted between the plates? (b) What will the capacitance be after the dielectric is inserted? (c) What is the permittivity of mica?