dielectric slab with thickness d is inserted halfway into the capacitor in the example (covering half the area). Given that d = 0.4 cm, A = 38 cm2, and ? = 4, find the equivalent capacitance in pF.

A capacitor is constructed out of two circular plates, each of radius 6 cm.  The plates are separated by 6.6 mm.  The space between the plates is filled with a dielectric of relative permittivity 1.3.  Calculate the capacitance, neglecting edge effects, in units of 10-12 F (that is, picofarads).  Use that the permittivity of free space is 8.85 x 10-12 F/m. (Please answer to the fourth decimal place - i.e 14.3225)

A parallel plate capacitor has the space between its plates filled with 1.4 mm of paper and 3.9 mm of teflon, as shown in the figure on the right. If the area of the plate of a capacitor is 9.2 cm², what is the capacitance of the capacitor? (Express your answer in pF (i.e. picofarads) Answer:

A parallel-plate capacitor is constructed by filling the space between two square plates with a block of three dielectric materials, as shown in the figure below. You may assume that ℓ ≫ d. A parallel-plate capacitor is comprised of two square plates with sides of length ℓ and separation distance d. There are three dielectric materials in the space between the capacitor plates. A material with length ℓ⁄2, height d, and dielectric constant ?1 fills the left half of the space. A material with length ℓ⁄2, height d⁄2, and dielectric constant ?2 fills the top right quarter of the space. A material with length ℓ⁄2, height d⁄2, and dielectric constant ?3 fills the bottom right quarter of the space.   (a) Find an expression for the capacitance of the device in terms of the plate area A and d, ?1, ?2, and ?3. (Use the following as necessary: ?1, ?2, ?3, ?0, A and d.)C =        (b) Calculate the capacitance using the values A = 1.30 cm2, d = 2.00 mm, ?1 = 4.90, ?2 = 5.60, and ?3 = 2.50.

A capacitor is attached to a battery. It has initial capacitance Co, voltage Vo, charge Qo, and energy Uo. Let's put some dielectric material of dielectric constant K in there in two different ways. For each case, figure out the following for the resulting "new" capacitor: C, V, Q, and U, in terms of the old value and K. The capacitor is left attached to the battery. A slab of dielectric material with K=3 is inserted into the capacitor without otherwise disturbing it. In terms of the initial values, what are the new values? The capacitor is disconnected from the battery after it is charged up to Qo. Then, a slab of dielectric material with K=3 is inserted into the capacitor without anybody touching the plates or otherwise disturbing the capacitor. In terms of the initial values, what are the new values?

In the diagram, an isolated charged parallel-plate capacitor holding charge Q isarranged horizontally, with one plate flush with a frictionless surface. The capacitor hascapacitance Co when there is no dielectric inserted. The dielectric block (mass m, dielectricconstant k) inside the capacitor is attached to a hanging block (mass M) by a massless stringrouted over a frictionless pulley. The length of the capacitor plates and dielectric block is Lalong the direction of motion. Assume there is no friction between the dielectric and thecapacitor plates.a. The blocks are initially at rest and the dielectric is initially completely inside thecapacitor. Use conservation of mechanical energy to determine the speed v of thefalling block at the moment the dielectric block completely exits the capacitor plates(in other words, determine a formula for the speed in terms of the variousparameters that have been defined as algebraic variables).b. Use your result from part a to find the minimum mass…

The electric field between the inner and the outer surfaces of a cylindrical capacitor carrying charge Q is given by È - Eo, where E, is a constant, r is the cylindrical radial coordinate and f is the corre- sponding unit vector. The inner and the outer radii of the capacitor are a and b, respeetively. Find the capacitance of the cylindrical capacitor. Select one: Eo QIn(b/a) Eo In(b/a) In(b/a) Q In(b/a) Eo E, In(b/a)

A spherical conductor of radius a and charge Q is concentric with spherical shell of negligible thickness, radius b > a, and charge -Q (as shown in the figure). Show that the capacitance of this cylindrical capacitor is C = 4πɛ0 ab/b-a

Two parallel plates having equal and opposite charges with area L x L, separation d is filled with a dielectric material as shown in the Figure. The related dielectric constant varies with x as x = a + [x]. Here, a = 100 cm, b = 54 cm, d = 0.88 cm and L= 1 m are given. Find the capacitance of this capacitor in 10-11 Farad. Take Eo 10 C²/Nm². Answer:

Express your answer to at least three decimal places.