Exam 26: Charge Separation and Storage

An isolated air-filled parallel-plate capacitor that is no longer connected to anything has been charged up to Q = 2.9 nC.The separation between the plates initially is 1.20 mm,and for this separation the capacitance is 31 pF.Calculate the work that must be done to pull the plates apart until their separation becomes 5.30 mm,if the charge on the plates remains constant.(ε₀ = 8.85 × 10^-12 C²/N • m²)

The electric field between square the plates of a parallel-plate capacitor has magnitude E.The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation,which is small compared to the dimensions of the plates.The magnitude of the electric field between the plates is now equal to

Each plate of a parallel-plate air-filled capacitor has an area of 0.0020 m²,and the separation of the plates is 0.020 mm.An electric field of 3.9 × 10⁶ V/m is present between the plates.What is the surface charge density on the plates? (ε₀ = 8.85 × 10^-12 C²/N • m²)

Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m²,and the separation of the plates is 0.080 mm.An electric field of 5.3 × 10⁶ V/m is present between the plates.What is the energy density between the plates? (ε₀ = 8.85 × 10^-12 C²/N • m²)

A charged capacitor stores energy U.Without connecting this capacitor to anything,dielectric having dielectric constant K is now inserted between the plates of the capacitor,completely filling the space between them.How much energy does the capacitor now store?

A parallel-plate capacitor consists of two parallel,square plates that have dimensions 1.0 cm by 1.0 cm.If the plates are separated by 1.0 mm,and the space between them is filled with teflon,what is the capacitance of this capacitor? (The dielectric constant for teflon is 2.1,and ε₀ = 8.85 × 10^-12 C²/N • m².)

The charge on the square plates of a parallel-plate capacitor is Q.The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation,which is small compared to the dimensions of the plates.The amount of charge on the plates is now equal to

An air-filled capacitor stores a potential energy of 6.00 mJ due to its charge.It is accidentally filled with water in such a way as not to discharge its plates.How much energy does it continue to store after it is filled? (The dielectric constant for water is 78 and for air it is 1.0006.)

A cylindrical capacitor is made of two thin-walled concentric cylinders.The inner cylinder has radius r₁ = 4.0 mm,and the outer one a radius r₂ = 8.0 mm.The common length of the cylinders is L = 150 m. What is the potential energy stored in this capacitor when a potential difference 4.0 V is applied between the inner and outer cylinder? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

A charge of 2.00 μC flows onto the plates of a capacitor when it is connected to a 12.0-V potential source. What is the minimum amount of work that must be done in charging this capacitor?

Equal but opposite charges Q are placed on the square plates of an air-filled parallel-plate capacitor.The plates are then pulled apart to twice their original separation,which is small compared to the dimensions of the plates.Which of the following statements about this capacitor are true? (There may be more than one correct choice.)

A 1.0 μF capacitor has a potential difference of 6.0 V applied across its plates.If the potential difference across its plates is increased to 8.0 V,how much ADDITIONAL energy does the capacitor store?

An air-filled parallel-plate capacitor is connected to a battery and allowed to charge up.Now a slab of dielectric material is placed between the plates of the capacitor while the capacitor is still connected to the battery.After this is done,we find that