The plates of a parallel-plate capacitor have a separation of 4.28 mm, and each has an area of 16.2 cm². Each plate carries a charge of magnitude 5.35x10-8 C. The plates are in vacuum. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Properties of a parallel-plate capacitor. What is the capacitance? Express your answer with the appropriate units. C = 3.35x10-12 F Submit ✓ Correct Part B Previous Answers Set Up: C =- C € A d Solve: C = 0 = €0 V= 2.310-10 What is the potential difference between the plates? Express your answer with the appropriate units. Part C E= and V = Ed. Submit Previous Answers Request Answer 1.62x10-³ m² 4.28x10-³ m UA X Incorrect; Try Again; 5 attempts remaining Value V 3 3.35 x 10-12 F What is the magnitude of the electric field between the plates? Express your answer with the appropriate units. ? Units ?

2. In lecture we saw parallel plate and coaxial cylindrical capacitors. We can also have spherical capacitors! Consider a conducting sphere with radius a and total charge Q enclosed within a concentric hollow spherical conducting shell with radius 6 and a total charge -Q. For parts a) and b), the region between the conductors (a < r < b) is empty (vacuum). a) Find an expression for the capacitance of a spherical capacitor. Is it geometric as we expect? b) Find an expression for the energy stored by the spherical capacitor first by using U (just replace C by your answer from part a)) and second by integrating the energy density u of the electric field over all space. Do your answers agree? = 20 c) Now suppose the region between the conductors is filled with a dielectric with dielectric constant ‹ = 3. What is the bound charge per unit area near the inner sphere (at r = = a) and near the outer shell (at r = b)? What is the total bound charge at each surface (expressed as a fraction of…

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. What is the capacitance (in µF) of a parallel plate capacitor having plates of area 1.25 m2 that are separated by 0.0230 mm of neoprene rubber? B.What charge (in µC) does it hold when 9.00 V is applied to it?

A parallel-plate air capacitor has a capacitance of 920 pF. The charge on each plate is 3.90 μC. Part A What is the potential difference between the plates? Express your answer with the appropriate units. V = Submit Part B V = 123+ Part C Submit AU = Value If the charge is kept constant, what will be the potential difference between the plates if the separation is doubled? Express your answer with the appropriate units. 123+ Submit Request Answer Value Units 3 123+ Value 3 ? Request Answer ( 3 ? How much work is required to double the separation? Express your answer with the appropriate units. Units - C ? Units Request Answer

The plates of a parallel-plate capacitor are 3.22 mm apart, and each has an area of 9.92 cm². Each plate carries a charge of magnitude 4.50x10-8 C. The plates are in vacuum. ▼ What is the capacitance? Express your answer with the appropriate units. C = Submit Part B PHÅ V = Value Request Answer What is the potential difference between the plates? Express your answer with the appropriate units. 98 Value C μᾶ Units Units ? ?

A parrallel plate capacitor consisting of two 30.0 cm x 30.0 cm square conductors are separated by a 3.00 mm piece of mica (k=5.00) is charged by a connecting it to an 18.0 V battery. What is the capacitance of this capacitor? What is the charge on the capacitor? If the mica is removed and replaced with glass (k=7.00), what is the potential difference of the plates now? What is the charge on the capacitor now with the glass?

A (4.000x10^2) µF capacitor is fully-charged when it has (9.6x10^-3) C on its plates. What is the potential difference across the plates of the capacitor? Give your answer in V using scientific notation.

Consider the equipotential map shown below. Estimate the magnitude of the E-field at point A. What direction is the E-field at point A? Rank the points A, B, and C in terms of their E-field strength. Sketch the electric field lines. What is the sign of the charge (+ or −) within the 30 V equipotential?

A 7.5 nF capacitor has 8.5 μJ of energy stored in its electric field. If the capacitor fully discharges in 0.1ms how much charge in nC will be released? Round your answer to the nearest integer.