Chapter 24

Capacitance andDielectricsLecture 1

Dr. Armen Kocharian

CapacitorsCapacitors are devices that store electric chargeExamples of where capacitors are used include:

radio receiversfilters in power suppliesenergy-storing devices in electronic flashes

Definition of CapacitanceThe capacitance, C, of a capacitor is defined as the ratio of the magnitude of the charge on either conductor to the potential difference between the conductors

The SI unit of capacitance is the farad (F)

QCV

=Δ

Makeup of a CapacitorA capacitor consists of two conductors

These conductors are called platesWhen the conductor is charged, the plates carry charges of equal magnitude and opposite directions

A potential difference exists between the plates due to the charge

C=Q/Vab Constant

If Q doubles (triples, quadruples...), the field doubles (triples, quadruples...)Then Vab also doubles (triples, quadruples...)But C=Q/Vab remains the same

conductora

conductorbsome random path

+Q

-Q

More About CapacitanceCapacitance will always be a positive quantityThe capacitance of a given capacitor is constantThe capacitance is a measure of the capacitor’s ability to store chargeThe farad is a large unit, typically you will see microfarads (μF) and picofarads (pF)

Parallel Plate CapacitorEach plate is connected to a terminal of the batteryIf the capacitor is initially uncharged, the battery establishes an electric field in the connecting wires

Parallel Plate Capacitor, contThis field applies a force on electrons in the wire just outside of the platesThe force causes the electrons to move onto the negative plateThis continues until equilibrium is achieved

The plate, the wire and the terminal are all at the same potential

At this point, there is no field present in the wire and the movement of the electrons ceases

Parallel Plate Capacitor, finalThe plate is now negatively chargedA similar process occurs at the other plate, electrons moving away from the plate and leaving it positively chargedIn its final configuration, the potential difference across the capacitor plates is the same as that between the terminals of the battery

Capacitance – Isolated Sphere

Assume a spherical charged conductorAssume V = 0 at infinity

Note, this is independent of the charge and the potential difference

4/ o

e e

Q Q RC πε RV k Q R k

= = = =Δ

Capacitance – Parallel Plates

The charge density on the plates is σ = Q/A

A is the area of each plate, which are equalQ is the charge on each plate, equal with opposite signs

The electric field is uniform between the plates and zero elsewhere

Capacitance – Parallel Plates, cont.

The capacitance is proportional to the area of its plates and inversely proportional to the distance between the plates

/o

o

ε AQ Q QCV Ed Qd ε A d

= = = =Δ

Parallel Plate Assumptions

The assumption that the electric field is uniform is valid in the central region, but not at the ends of the platesIf the separation between the plates is small compared with the length of the plates, the effect of the non-uniform field can be ignored

Energy in a Capacitor –Overview

Consider the circuit to be a systemBefore the switch is closed, the energy is stored as chemical energy in the batteryWhen the switch is closed, the energy is transformed from chemical to electric potential energy

Energy in a Capacitor –Overview, cont

The electric potential energy is related to the separation of the positive and negative charges on the platesA capacitor can be described as a device that stores energy as well as charge

Capacitance of a Cylindrical Capacitor,

From Gauss’s Law, the field between the cylinders isE = 2keλ / rΔV = -2keλ ln (b/a)The capacitance becomes

( )2 ln /e

QCV k b a

= =Δ

Capacitance of a Spherical Capacitor

The potential difference will be

The capacitance will be

1 1eV k Q

b a⎛ ⎞Δ = −⎜ ⎟⎝ ⎠

( )= = =

Δ −⎛ ⎞−⎜ ⎟⎝ ⎠

11 1 e

e

Q abCV k b ak

a b

⎡ ⎤ ⎛ ⎞− = − =− = = −⎜ ⎟⎢ ⎥⎣ ⎦ ⎝ ⎠∫ ∫ 21 1 1bb b

b a r e e eaa a

drV V E dr k Q k Q k Qr r b a

Circuit SymbolsA circuit diagram is a simplified representation of an actual circuitCircuit symbols are used to represent the various elementsLines are used to represent wiresThe battery’s positive terminal is indicated by the longer line

Connecting capacitors togetherTwo ways of connecting capacitors together:

VaVa VbVb

in parallel in series

Capacitors in ParallelWhen capacitors are first connected in the circuit, electrons are transferred from the left plates through the battery to the right plate, leaving the left plate positively charged and the right plate negatively charged

Capacitors in Parallel, 2The flow of charges ceases when the voltage across the capacitors equals that of the batteryThe capacitors reach their maximum charge when the flow of charge ceasesThe total charge is equal to the sum of the charges on the capacitors

Qtotal = Q1 + Q2

The potential difference across the capacitors is the same

And each is equal to the voltage of the battery

Capacitors in Parallel, 3The capacitors can be replaced with one capacitor with a capacitance of Ceq

The equivalent capacitor must have exactly the same external effect on the circuit as the original capacitors

Capacitors in Parallel, finalCeq = C1 + C2 + … The equivalent capacitance of a parallel combination of capacitors is greater than any of the individual capacitors

Essentially, the areas are combined

Equivalent Capacitance, Example

The 1.0-μF and 3.0-μF capacitors are in parallel as are the 6.0-μF and 2.0-μF capacitorsThese parallel combinations are in series with the capacitors next to themThe series combinations are in parallel and the final equivalent capacitance can be found

Capacitors in parallel

The potential difference across the two capacitors is the sameQ1 = C1Vab and Q2 = C2 VabTherefore, Q=Q1+Q2 = (C1 + C2) VabThis is equivalent to

equivalent capacitance

Capacitors in SeriesWhen a battery is connected to the circuit, electrons are transferred from the left plate of C1 to the right plate of C2through the battery

Capacitors in Series, 2As this negative charge accumulates on the right plate of C2, an equivalent amount of negative charge is removed from the left plate of C2, leaving it with an excess positive chargeAll of the right plates gain charges of –Qand all the left plates have charges of +Q

Capacitors inSeries, 3An equivalent capacitor can be found that performs the same function as the series combinationThe potential differences add up to the battery voltage

Capacitors in Series, finalQ = Q1 + Q2 + …ΔV = V1 + V2 + …

The equivalent capacitance of a series combination is always less than any individual capacitor in the combination

1 2

1 1 1

eqC C C= + +…

These two plates areconnected

Capacitors in series

The two connected plates effectively form a single conductorThus, the two connected plates have equal and opposite charge

Capacitors in series (cont.)

Va VbQ -Q Q -Q

Remember, definition:Thus, this is entirely equivalent to

Va VbQ -Q

Ceq

equivalent capacitance

For more than two capacitors in parallel or in serees the results generalize to

Problem-Solving HintsBe careful with the choice of units

In SI, capacitance is in farads, distance is in meters and the potential differences are in voltsElectric fields can be in V/m or N/C

When two or more capacitors are connected in parallel, the potential differences across them are the same

The charge on each capacitor is proportional to its capacitanceThe capacitors add directly to give the equivalent capacitance

Problem-Solving Hints, contWhen two or more capacitors are connected in series, they carry the same charge, but the potential differences across them are not the same

The capacitances add as reciprocals and the equivalent capacitance is always less than the smallest individual capacitor

Energy Stored in a CapacitorAssume the capacitor is being charged and, at some point, has a charge q on itThe work needed to transfer a charge from one plate to the other is

The total work required is

qdW Vdq dqC

= Δ =

2

0 2Q q QW dq

C C= =∫

Energy, contThe work done in charging the capacitor appears as electric potential energy U:

This applies to a capacitor of any geometryThe energy stored increases as the charge increases and as the potential difference increasesIn practice, there is a maximum voltage before discharge occurs between the plates

221 1 ( )

2 2 2QU Q V C VC

= = Δ = Δ

Energy, finalThe energy can be considered to be stored in the electric field For a parallel-plate capacitor, the energy can be expressed in terms of the field as U = ½ (εoAd)E2

It can also be expressed in terms of the energy density (energy per unit volume)uE = ½ εoE2

Find the equivalent capacitance of this network.

C1 C2

C3The trick here is to take it one step at a timeC1 and C3 are in series. So this circuit is equivalent to

C3

C4

Example

Then, this is equivalent to

Ceq

Another exampleFind the equivalent capacitance of this network.

C1

C2

C3

C4

C3

C4C5

Again, take it in steps. C1 and C2 are in series. So this is equivalent to

C3

C4C5

Now this looks a little different than what we have seen.But it is just three capacitors in parallel. We can redraw it as

C3 C5C4

which is equivalent toCeq

Energy stored in a capacitorA capacitor stores potential energyBy conservation of energy, the stored energy is equal to the work done in charging up the capacitorOur goal now is to calculate this work, and thus the amount of energy stored in the capacitor

Once the capacitor is charged

Let q and v be the charge and potential of the capacitor at some instant while it is being charged

q<Q and v<V, but still v=q/CIf we want to increase the charge from q q+dq, we need to do an amount of work dW

The total work done in charging up the capacitor is

Potential energy stored in the capacitor is

Energy in the electric fieldIf a capacitor is charged, there is an electric field between the two conductors

We can think of the energy of the capacitor as being stored in the electric fieldFor a parallel plate capacitor, ignoring edge effects, the volume over which the field is active is Axd

Then, the energy per unit volume (energy density) is

But the capacitance and electric field are given by

Putting it all together:

This is the energy density (energy per unit volume) associated with an electric field

Derived it for parallel plate capacitor, but valid in general

ProblemCapacitors C1 = 6 μF, C2 = 3 μF and ΔV= 20 V are given. Capacitor C1 are first charged by closing switch S1 . Switch S1 then is opened and the charged capacitor is connected to uncharged capacitor C2 by closing switch S2(C1>C2) Find the initial charge acquired by C1 and the final charge on each capacitor.

ExampleQ1i = Q initial charge of C1 = C1VQ1f = final charge of C1Q2f = final charge of C2Charge Qtotal = Q1i + Q2i

After we close the switches, this chargeWill distribute itself partially on C1 andpartiallyon C2, but with Qtotal = Q1f + Q2f

QC

V=

Δ66.00 10

20.0Q−× =

120 CQ μ=

1 2120 CQ Qμ= −1 2Q Q Q+ =

QV

CΔ =

2 2

1 2

120 Q QC C−

=

1

1 2

1 2

V VQ QC C

Δ = Δ

=

( )( ) ( )2 23.00 120 6.00Q Q− =

2360

40.0 C9.00

Q μ= =

1 120 C 40.0 C 80.0 CQ μ μ μ= − =

Example

- +

C1 and C2 (C1>C2) are both charged to potential V, but withopposite polarity. They are removed from the battery, and are connected as shown. Then we close the two switchesFind Vab after the switches have been closed

Q1i = initial charge of C1 = C1VQ2i = initial charge of C2 = - C2V

Charge Qtotal = Q1i + Q2i = (C1-C2)V

After we close the switches, this charge willdistribute itself partially on C1 and partiallyon C2, but with Qtotal = Q1f + Q2f

+Q1f -Q1f

-Q2f+Q2f

Qtotal = Q1i + Q2i = (C1-C2)V=Q1f + Q2f

Q1f = C1 VabQ2f = C2 Vab

Q1f + Q2f = (C1 + C2) Vab

Then, equating the two boxed equations

Now calculate the energy before and after

Ebefore = ½ C1 V2 + ½ C2 V2 = ½ (C1 + C2) V2

Eafter = ½ Ceq Vab, where Ceq is the equivalent capacitance of the circuit after the switches have been closed

C1 and C2 are in parallelCeq = C1 + C2

Eafter = ½ (C1 + C2) Vab

What happens to conservation of energy????It turns out that some of the energy is radiated as electromagnetic waves!!

Some Uses of CapacitorsDefibrillators

When fibrillation occurs, the heart produces a rapid, irregular pattern of beatsA fast discharge of electrical energy through the heart can return the organ to its normal beat pattern

In general, capacitors act as energy reservoirs that can be slowly charged and then discharged quickly to provide large amounts of energy in a short pulse

Capacitors with DielectricsA dielectric is a nonconducting material that, when placed between the plates of a capacitor, increases the capacitance

Dielectrics include rubber, plastic, and waxed paper

For a parallel-plate capacitor, C = κCo = κεo(A/d)

The capacitance is multiplied by the factor κ when the dielectric completely fills the region between the plates

Dielectrics, contIn theory, d could be made very small to create a very large capacitanceIn practice, there is a limit to d

d is limited by the electric discharge that could occur though the dielectric medium separating the plates

For a given d, the maximum voltage that can be applied to a capacitor without causing a discharge depends on the dielectric strength of the material

Dielectrics, finalDielectrics provide the following advantages:

Increase in capacitanceIncrease the maximum operating voltagePossible mechanical support between the plates

This allows the plates to be close together without touchingThis decreases d and increases C

Types of Capacitors – Tubular

Metallic foil may be interlaced with thin sheets of paper or MylarThe layers are rolled into a cylinder to form a small package for the capacitor

Types of Capacitors – Oil Filled

Common for high-voltage capacitorsA number of interwoven metallic plates are immersed in silicon oil

Types of Capacitors –Electrolytic

Used to store large amounts of charge at relatively low voltagesThe electrolyte is a solution that conducts electricity by virtue of motion of ions contained in the solution

Types of Capacitors –Variable

Variable capacitors consist of two interwoven sets of metallic platesOne plate is fixed and the other is movableThese capacitors generally vary between 10 and 500 pFUsed in radio tuning circuits

Capacitor typesCapacitors are often classified by the materials used between electrodesSome types are air, paper, plastic film, mica, ceramic, electrolyte, and tantalumOften you can tell them apart by the packaging

Plastic Film Capacitor

Ceramic CapacitorTantalum Capacitor

Electrolyte Capacitor

Electric DipoleAn electric dipole consists of two charges of equal magnitude and opposite signsThe charges are separated by 2aThe electric dipole moment (p) is directed along the line joining the charges from –q to +q

Electric Dipole, 2The electric dipole moment has a magnitude of p = 2aqAssume the dipole is placed in a uniform external field, E

E is external to the dipole; it is not the field produced by the dipole

Assume the dipole makes an angle θwith the field

Electric Dipole, 3Each charge has a force of F = Eqacting on itThe net force on the dipole is zeroThe forces produce a net torque on the dipole

Electric Dipole, finalThe magnitude of the torque is:τ = 2Fa sin θ = pE sin θThe torque can also be expressed as the cross product of the moment and the field: τ = p x EThe potential energy can be expressed as a function of the orientation of the dipole with the field: Uf – Ui = pE(cos θi – cos θf) →U = - pE cos θ = - p · E

Polar vs. Nonpolar MoleculesMolecules are said to be polarized when a separation exists between the average position of the negative charges and the average position of the positive chargesPolar molecules are those in which this condition is always presentMolecules without a permanent polarization are called nonpolar molecules

Water MoleculesA water molecule is an example of a polar moleculeThe center of the negative charge is near the center of the oxygen atomThe x is the center of the positive charge distribution

Polar Molecules and DipolesThe average positions of the positive and negative charges act as point chargesTherefore, polar molecules can be modeled as electric dipoles

Induced PolarizationA symmetrical molecule has no permanent polarization (a)Polarization can be induced by placing the molecule in an electric field (b)Induced polarization is the effect that predominates in most materials used as dielectrics in capacitors

Dielectrics – An Atomic ViewThe molecules that make up the dielectric are modeled as dipolesThe molecules are randomly oriented in the absence of an electric field

Dielectrics – An Atomic View, 2

An external electric field is appliedThis produces a torque on the moleculesThe molecules partially align with the electric field

Dielectrics – An Atomic View, 3

The degree of alignment of the molecules with the field depends on temperature and the magnitude of the fieldIn general,

the alignment increases with decreasing temperaturethe alignment increases with increasing field strength

Dielectrics – An Atomic View, 4

If the molecules of the dielectric are nonpolar molecules, the electric field produces some charge separationThis produces an induced dipole momentThe effect is then the same as if the molecules were polar

Dielectrics – An Atomic View, final

An external field can polarize the dielectric whether the molecules are polar or nonpolarThe charged edges of the dielectric act as a second pair of plates producing an induced electric field in the direction opposite the original electric field

Induced Charge and FieldThe electric field due to the plates is directed to the right and it polarizes the dielectricThe net effect on the dielectric is an induced surface charge that results in an induced electric fieldIf the dielectric were replaced with a conductor, the net field between the plates would be zero

Geometry of Some Capacitors

Chapter 26

Capacitance and Dielectrics

Quick Quiz 26.1

A capacitor stores charge Q at a potential difference ΔV. If the voltage applied by a battery to the capacitor is doubled to 2ΔV:

(a) the capacitance falls to half its initial value and the charge remains the same

(b) the capacitance and the charge both fall to half their initial values

(c) the capacitance and the charge both double

(d) the capacitance remains the same and the charge doubles

Answer: (d). The capacitance is a property of the physical system and does not vary with applied voltage. According to Equation 26.1, if the voltage is doubled, the charge is doubled.

Quick Quiz 26.1

Quick Quiz 26.2

Many computer keyboard buttons are constructed of capacitors, asshown in the figure below. When a key is pushed down, the soft insulator between the movable plate and the fixed plate is compressed. When the key is pressed, the capacitance

(a) increases

(b) decreases

(c) changes in a way that we cannot determine because the complicated electric circuit connected to the keyboard button may cause a change in ΔV.

Answer: (a). When the key is pressed, the plate separation is decreased and the capacitance increases. Capacitance depends only on how a capacitor is constructed and not on the external circuit.

Quick Quiz 26.2

Quick Quiz 26.3

Two capacitors are identical. They can be connected in series or in parallel. If you want the smallest equivalent capacitance for the combination, you should connect them in

(a) series

(b) parallel

(c) Either combination has the same capacitance.

Answer: (a). When connecting capacitors in series, the inverses of the capacitances add, resulting in a smaller overall equivalent capacitance.

Quick Quiz 26.3

Quick Quiz 26.4

Consider the two capacitors in question 3 again. Each capacitor is charged to a voltage of 10 V. If you want the largest combined potential difference across the combination, you should connect them in

(a) series

(b) parallel

(c) Either combination has the same potential difference.

Answer: (a). When capacitors are connected in series, the voltages add, for a total of 20 V in this case. If they are combined in parallel, the voltage across the combination is still 10 V.

Quick Quiz 26.4

Quick Quiz 26.5

You have three capacitors and a battery. In which of the following combinations of the three capacitors will the maximum possible energy be stored when the combination is attached to the battery?

(a) series

(b) parallel

(c) Both combinations will store the same amount of energy.

Answer: (b). For a given voltage, the energy stored in a capacitor is proportional to C: U = C(ΔV)2/2. Thus, you want to maximize the equivalent capacitance. You do this by connecting the three capacitors in parallel, so that the capacitances add.

Quick Quiz 26.5

Quick Quiz 26.6

You charge a parallel-plate capacitor, remove it from the battery, and prevent the wires connected to the plates from touching each other. When you pull the plates apart to a larger separation, do the following quantities increase, decrease, or stay the same? (a) C; (b) Q; (c) E between the plates; (d) ΔV ; (e) energy stored in the capacitor.

Answer: (a) C decreases (Eq. 26.3). (b) Q stays the same because there is no place for the charge to flow. (c) E remains constant (see Eq. 24.8 and the paragraph following it). (d) ΔV increases because ΔV = Q/C, Q is constant (part b), and C decreases (part a). (e) The energy stored in the capacitor is proportional to both Q and ΔV (Eq. 26.11) and thus increases. The additional energy comes from the work you do in pulling the two plates apart.

Quick Quiz 26.6

Quick Quiz 26.7

Repeat Quick Quiz 26.6, but this time answer the questions for the situation in which the battery remains connected to the capacitor while you pull the plates apart.

Answer: (a) C decreases (Eq. 26.3). (b) Q decreases. The battery supplies a constant potential difference ΔV; thus, charge must flow out of the capacitor if C = Q /ΔV is to decrease. (c) E decreases because the charge density on the plates decreases. (d) ΔV remains constant because of the presence of the battery. (e) The energy stored in the capacitor decreases (Eq. 26.11).

Quick Quiz 26.7

Quick Quiz 26.8

If you have ever tried to hang a picture or a mirror, you know it can be difficult to locate a wooden stud in which to anchor your nail or screw. A carpenter’s stud-finder is basically a capacitor with its plates arranged side by side instead of facing one another, as shown in the figure below. When the device is moved over a stud, the capacitance will:

(a) increase

(b) decrease

Answer: (a). The dielectric constant of wood (and of all other insulating materials, for that matter) is greater than 1; therefore, the capacitance increases (Eq. 26.14). This increase is sensed by the stud-finder's special circuitry, which causes an indicator on the device to light up.

Quick Quiz 26.8

Quick Quiz 26.9

A fully charged parallel-plate capacitor remains connected to a battery while you slide a dielectric between the plates. Do the following quantities increase, decrease, or stay the same? (a) C; (b) Q; (c) E between the plates; (d) ΔV.

Answer: (a) C increases (Eq. 26.14). (b) Q increases. Because the battery maintains a constant ΔV, Q must increase if C increases. (c) E between the plates remains constant because ΔV = Ed and neither ΔV nor d changes. The electric field due to the charges on the plates increases because more charge has flowed onto the plates. The induced surface charges on the dielectric create a field that opposes the increase in the field caused by the greater number of charges on the plates (see Section 26.7). (d) The battery maintains a constant ΔV.

Quick Quiz 26.9

The positive charge is the end view of a positively charged glass rod. A negatively charged particle moves in a circular arc around the glass rod. Is the work done on the charged particle by the rod’s electric field positive, negative or zero?

1. Positive 2. Negative3. Zero

1. Positive 2. Negative3. Zero

The positive charge is the end view of a positively charged glass rod. A negatively charged particle moves in a circular arc around the glass rod. Is the work done on the charged particle by the rod’s electric field positive, negative or zero?

Rank in order, from largest to smallest, the potential energies Ua to Ud of these four pairs of charges. Each + symbol represents the same amount of charge.

1. Ua = Ub > Uc = Ud2. Ua = Uc > Ub = Ud3. Ub = Ud > Ua = Uc4. Ud > Ub = Uc > Ua5. Ud > Uc > Ub > Ua

Rank in order, from largest to smallest, the potential energies Ua to Ud of these four pairs of charges. Each + symbol represents the same amount of charge.

1. Ua = Ub > Uc = Ud2. Ua = Uc > Ub = Ud3. Ub = Ud > Ua = Uc4. Ud > Ub = Uc > Ua5. Ud > Uc > Ub > Ua

A proton is released from rest at point B, where the potential is 0 V. Afterward, the proton

1. moves toward A with an increasing speed. 2. moves toward A with a steady speed. 3. remains at rest at B. 4. moves toward C with a steady speed.5. moves toward C with an increasing speed.

1. moves toward A with an increasing speed.2. moves toward A with a steady speed. 3. remains at rest at B. 4. moves toward C with a steady speed.5. moves toward C with an increasing speed.

A proton is released from rest at point B, where the potential is 0 V. Afterward, the proton

Rank in order, from largest to smallest, the potentials Va to Ve at the points a to e.

1. Va = Vb = Vc = Vd = Ve2. Va = Vb > Vc > Vd = Ve3. Vd = Ve > Vc > Va = Vb4. Vb = Vc = Ve > Va = Vd5. Va = Vb = Vd = Ve > Vc

Rank in order, from largest to smallest, the potentials Va to Ve at the points a to e.

1. Va = Vb = Vc = Vd = Ve2. Va = Vb > Vc > Vd = Ve3. Vd = Ve > Vc > Va = Vb4. Vb = Vc = Ve > Va = Vd5. Va = Vb = Vd = Ve > Vc

Rank in order, from largest to smallest, the potential differences ∆V12, ∆V13, and ∆V23 between points 1 and 2, points 1 and 3, and points 2 and 3.

1. ∆V12 > ∆V13 = ∆V232. ∆V13 > ∆V12 > ∆V233. ∆V13 > ∆V23 > ∆V124. ∆V13 = ∆V23 > ∆V125. ∆V23 > ∆V12 > ∆V13

Rank in order, from largest to smallest, the potential differences ∆V12, ∆V13, and ∆V23 between points 1 and 2, points 1 and 3, and points 2 and 3.

1. ∆V12 > ∆V13 = ∆V232. ∆V13 > ∆V12 > ∆V233. ∆V13 > ∆V23 > ∆V124. ∆V13 = ∆V23 > ∆V125. ∆V23 > ∆V12 > ∆V13

Chapter 29Reading Quiz

What are the units of potential difference?

1. Amperes2. Potentiometers3. Farads4. Volts5. Henrys

What are the units of potential difference?

1. Amperes2. Potentiometers3. Farads4. Volts5. Henrys

New units of the electric field were introduced in this chapter. They are:

1. V/C. 2. N/C. 3. V/m. 4. J/m2.5. W/m.

New units of the electric field were introduced in this chapter. They are:

1. V/C. 2. N/C. 3. V/m.4. J/m2.5. W/m.

The electric potential inside a capacitor

1. is constant.2. increases linearly from the negative to

the positive plate.3. decreases linearly from the negative to

the positive plate.4. decreases inversely with distance from

the negative plate.5. decreases inversely with the square of the

distance from the negative plate.

The electric potential inside a capacitor

1. is constant.2. increases linearly from the negative to

the positive plate.3. decreases linearly from the negative to

the positive plate.4. decreases inversely with distance from

the negative plate.5. decreases inversely with the square of the

distance from the negative plate.