Exam 26: Potential and Field

A conducting sphere of radius R carries an excess positive charge and is very far from any other charges.Which one of the following graphs best illustrates the potential (relative to infinity)produced by this sphere as a function of the distance r from the center of the sphere?

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates.All the geometric parameters of the capacitor (plate diameter and plate separation)are now DOUBLED.If the original energy density between the plates was u₀,what is the new energy density?

A 6.00-μF parallel-plate capacitor has charges of ±40.0 μC on its plates.How much potential energy is stored in this capacitor?

Three capacitors,with capacitances = 4.0 μF, = 3.0 μF,and = 2.0 μF,are connected to a 12 -V voltage source,as shown in the figure.What is the charge on capacitor ?

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?

An air-filled capacitor stores a potential energy of 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 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?

Three capacitors,of capacitance 5.00 μF,10.0 μF,and 50.0 μF,are connected in series across a 12.0-V voltage source. (a)How much charge is stored in the 5.00-μF capacitor? (b)What is the potential difference across the 10.0-μF capacitor?

If the potential in a region is given by V(x,y,z)= xy - 3z^-2,then the y component of the electric field in that region is

The graph in the figure shows the variation of the electric potential V (measured in volts)as a function of the radial direction r (measured in meters).For which range or value of r is the magnitude of the electric field the largest?

A conducting sphere contains positive charge distributed uniformly over its surface.Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity.(There may be more than one correct choice.)

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)

When two or more capacitors are connected in parallel across a potential difference,

The graph in the figure shows the variation of the electric potential V(x)(in arbitrary units)as a function of the position x (also in arbitrary units).Which of the choices below correctly describes the orientation of the x-component of the electric field along the x-axis?

In the circuit shown in the figure,all the capacitors are air-filled.With the switch S open,the 40.0-µF capacitor has an initial charge of 5.00 µC while the other three capacitors are uncharged.The switch is then closed and left closed for a long time.Calculate the initial and final values of the total electrical energy stored in these four capacitors.

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

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

The capacitive network shown in the figure is assembled with initially uncharged capacitors.A potential difference,V_ab = +100V,is applied across the network.The switch S in the network is kept open.Assume that all the capacitances shown are accurate to two significant figures.What is potential difference V_cd across the open switch S?

The potential as a function of position x is shown in the graph in the figure.Which statement about the electric field is true?

A parallel-plate capacitor with plate separation of 1.0 cm has square plates,each with an area of 6.0 × 10^-2 m².What is the capacitance of this capacitor if a dielectric material with a dielectric constant of 2.4 is placed between the plates,completely filling them? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)