Chapter 17 Electric Potential and Electric Energy; Capacitance

Electric Potential and Electric Energy; Capacitance

Review of Chapter 1617.1 Electric Potential and Potential Difference17.2 Relationship between Electric Potential and Electric

Field17.3 Equipotential Lines17.4 The Electron Volt, a Unit of Energy17-5 Electric Potential Due to Point Charges17-6 Electric Dipoles17-7 Capacitance17-8 Dielectrics17-9 Storage of Electric Charge17-10 Cathode Ray Tube17-11 The Electrocardiogram

Important stuff from Chapter 16:Coulomb’s Law: F = kQ1Q2/r

2

where:k = 9.0 x 109 Nm2/C2 Q1 & Q2 are two charges (coulomb)

r = distance between two charges

Important stuff from Chapter 16:Electric Field (E)—force (F) exerted on a

positive test charge divided by the magnitude of the charge (q, coulombs)

E = F/q (units N/C) electric field goes from positive to

negative (the path of a positive test charge)

Important stuff from Chapter 16:Electric Field due to a Point Charge:

E = kQ/r2

Important stuff from Chapter 16:Electric potential energy—the energy

stored in a charged objects when its in an electric field

positive when the two charges are the same (repulsive) and negative when the two charges are opposite (attractive)

Electric Potential and Potential DifferenceTo move an charge in an electric field work

must be done.

Electric Potential and Potential Difference   change in electric potential

energy (PEa – PEb) when a charge, q, moves from point b to point a is the negative work done by the electric force to move the charge from b to a

  PE of a charge is the largest when it is closest to the plate with the same charge

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b a

Electric Potential and Potential Difference

Electric Potential (potential)—the potential energy per unit charge (V)

Va = PEa/q --for a test charge, q, at point a in an electric field

Where is the test charge’s electric potential the most, at point a or b?Positive plate has higher potential

than negative (by definition, why?)

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b a

Electric Potential and Potential Difference

Can only measure differences in PE; so can measure the potential difference (difference in potential) between two points

Since potential difference (PEa – PEb) = W then

Vab = Va Vb = Wba/q

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b a

Electric Potential and Potential Difference

Vab = Va Vb = Wba/q Unit; volt (1 V = 1 J/C) Voltage = potential

differenceZero for voltage is

arbitrary since we can only measure PE

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b a

Electric Potential and Potential Difference Since electric potential (V) =

PE/q then PE = PEb PEa = qVba

if an object with charge q moves through a potential difference Vba its potential energy changes by an amount qVba

electric potential difference is a measure of how much energy an electric charge can acquire in a situation and also a measure of how much work a charge can do

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b a

Electric Potential and Potential Difference

Accelerating a charge; PE = qV = KE so

v = (2qV/m) since KE = ½ mv2

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b a

Relationship between Electric Potential and Electric FieldIn a uniform electric field (parallel plates) to

move a charge:W = qV = Fd = qEd (since F = Eq) so V = Ed or E (electric field) = V/d

Equipotential Lines Equipotential lines—graphic

representation of electric potential Potential the same on lines so it takes no

work to move charges along the lines Always perpendicular to field lines

(diagram p.507) Continuous lines, never end A conductor must be entirely at the same

potential in the static case or electrons would accumulate at its surface

Equipotential Lines

Equipotential lines—graphic representation of electric potential

Always perpendicular to field lines (diagram p.507)

The Electron Volt; Unit of Energy Electron Volt (eV)—used to measure very

small energies (electrons, atoms, molecules, etc.)

Energy acquired by a particle carrying the charge of one electron as a result of moving through a potential difference of 1 volt

1 eV = 1.6 x 1019 J (qe = 1.6 x 1019 C)

electrons accelerated through potential difference of 10V loses 10V of PE and gains 10V of KE

Electric Potential due to Point Charges V = kQ/r where Q = point charge, r =

distance between point and test charge and k = ?

V represents the absolute potential since the V at r = equals zero

So V Q and V 1/r but E1/r2 (remember E = kQ/r2)

Electric Dipoles electric dipole--two equal point charges (Q)

of opposite sign separated by a distancedipole moment--the product of charge times

length (Ql)polar molecules—molecules that have a

dipole moment

Capacitance capacitor—a device that can store electric

charge consists of two conducting objects placed

near each other but not touching widely used in electronic: camera flash,

surge protectors, energy backups, memory for binary code (RAM)

often consists of two parallel plates (of area A, and separation d) rolled together with an insulating material between them

symbol : —||—

Capacitance

CapacitorsLeydon Jar

Capacitance capacitor—a device that can store electric

charge (diagram)

Capacitance Amount of charge acquired by a given

capacitor

Q = CV where:

Q = amt. of charge (C)V = potential difference (V)C = capacitance of capacitor (constant of

proportionality dependent on properties of capacitor)--units farad (F) = Coulombs/Volts

Capacitance For a parallel plate capacitor: C = oA/d where:

o = permittivity of free space = 8.85 x 1012 C2/Nm2 (remember)

Dielectrics Dielectric—the insulating sheet between the

plates of a capacitorServes several purposes:

Allows higher voltages to be applied without charge passing the gap, dielectrics break down less readily than air

Allows plates to be closer together, the closer the plates are the larger the capacitance of the capacitor (WHY?)

Dielectrics For a parallel plate capacitor: C = KoA/d where:

K = dielectric constant (Table 17-3) Since C = oA/d then

= Ko where:

= the permittivity of the material

Dielectrics Molecular Description of dielectricsWith air between plates; only plates of

capacitor have a potential difference

Dielectrics Molecular Description of

dielectricsWith a dielectric;

molecules of dielectric can line up in electric field of capacitor plates causing a net negative side by positive plate and a net positive by negative plate (even though charges do not move in dielectric material—insulator)

Dielectrics

Molecular Description of dielectrics

A positive test charge within the dielectric does not feel the full force of the electric field of the capacitor so it takes a greater potential difference between the two plates of the capacitor to cause it to move in the dielectric

Storage of Electric EnergyA charged capacitor stores electric energyThe net effect of charging a capacitor is to

remove charge from one plate and add it to another (using a source of electricity—battery)

Storage of Electric EnergyA capacitor is not charged instantly—it

requires time and work to do this and this increases with increasing charge on plates (?)

If the work were constant then the work required to charge a capacitor would be W = QV

But since it is not we deal with the average voltage (1/2 of Vf + VI) so

W = Q Vf/2 (why?)

Storage of Electric EnergyInternal energy stored in a capacitor is: U = 1/2QV where:V is potential difference between plates Since Q = CV then: U = ½ Q2/Cand since C = oA/d & V = Ed

then U = 1/2oE2 A/d

Storage of Electric EnergyEnergy density (u)—energy per unit volume u = energy/volume = 1/2 oE

2

Cathode Ray TubeRead section 17-10 and know this:What is a CRT?What is thermionic emission?What is a cathode?What is an anode?Explain how a cathode ray tube works.What is an oscilloscope?Explain how an electrocardiogram measures

heart function.Extra Credit: Find out about LCD, LED and

Plasma screens (for TV’s)

Cathode Ray Tube

Explain how a cathode ray tube works.

Cathode Ray Tube

What is an oscilloscope?

The ElectrocardiogramExplain how an electrocardiogram measures

heart function.