Capacitance

Physics 102Professor Lee

CarknerLecture 12

At which times do you have a final (select all that apply)?

(These are the times for multi-section finals, don’t answer if you don’t have a final at any of these times.)

A) Monday 6-8pmB) Tuesday 6-8 pmC) Wednesday 6-8 pmD) Wednesday 3-5 pmE) Thursday 3-5 pmF) I have a multi-section final, but I don’t know when

PAL #11 Potential

Find potential 1 meter and 5 meters away from -7.00nC charge

V = kQ/r V1 = (8.99X109)(7X10-9)/1 = 62.93 V

V5 = (8.99X109)(7X10-9)/5 = 12.59 V

Change in potential energy between the two points

V = 62.93-12.59 = 50.34 V PE = qV = (1.6X10-19)(50.34) = 8.05X10-18 J

PAL #11 Potential

What is energy and velocity at 1 meter? Negative charge repels negative charge, so

electron slows down KEf = KEi - PE

KEi = ½mv2 = (0.5)(9.1X10-31)(8.77X106)2 = 3.50X10-17 J

KEf = 3.50X10-17 – 8.05X10-18 = 2.7X10-17 J

v = (2KEf/m)½ = [(2)(2.7X10-17)/(9.1X10-31)]½ = 7.7X106 m/s

PAL #11 Potential

(Optional part b) What is initial speed a long distance away?

For large distance away, V = 0 V = 12.95-0 = 12.95 V (between 5 meters and

very far away) PE = qV = (1.6X10-19)(12.95) = 2.07X10-18 J Energy at gun is equal to the energy at 5 meters plus

this PE

KEf = 3.50X10-17 + 2.07X10-18 = 3.71X10-17 J v = [(2)(3.71X10-17)/(9.1X10-31)]½ = 9.03X106

m/s

Equipotentials

Each line represents one value of V Particles moving along an

equipotential do not gain or lose energy

Equipotentials cannot cross

Blue = field = E

Dashed = potential = V

Capacitance A capacitor is a device that can store

charge and thus energy

The amount of charge depends on the potential difference across the capacitor and the intrinsic properties of the device This intrinsic property is called capacitance

and is represented by C

Capacitance Defined The amount of charge stored by a capacitor is just:

Q = C V Or, defining the capacitance:

C = Q/V

The units of capacitance are farads (F)1 F = 1 C/V

Typical capacitances are much less than a farad:

e.g. microfarad = F = 1 X 10-6 F

Capacitor Info A capacitor generally consists of two parallel metal

plates

Consider a battery connected across two metal plates

Electrons are attracted to the positive terminal and are lost by the second plate

Plates can’t touch or charge would move together and

cancel out

Capacitor Diagram

--

+ +V VQ

Capacitor Properties The capacitance depends

on four things:

The distance between them (d)

The dielectric constant of the material between the plates ()

The permittivity of free

space (0) A constant: 0 = 8.85 X 10-12

C2/N m2

C = 0(A/d)

Dielectrics in Capacitors

The properties of the material between the plates is important

The polarized material partially cancels out the electric field between the plates

Dielectrics

The dielectric reduces the effective voltage

A dielectric allows a capacitor to store more charge with the same voltage

The dielectric also allows you to move the plates closer together without touching

Breakdown The dielectric must be an insulator

If the voltage is large enough, the charge will jump across anyway

While Q = CV, there is a limit to how much we can increase Q by increasing V

Normally about 20 million volts

Energy in a Capacitor

Every little batch of charge increases the potential difference between the plates and increases the work to move the next batch

Charge stops moving when the V across the plates is equal to the max V possible for the circuit

Total Energy

Energy = 1/2 Q V =1/2 C (V)2 = Q2/2C since Q = C V

At very large V the capacitor will discharge by itself

Using Capacitors Capacitors store energy Generally only for short periods of time

Useful when you need a quick burst of energy

For a flash, capacitor is discharged into a gas (like xenon) that will glow when ionized

Since capacitance depends on d, can also use capacitance to measure separation

Next Time

Exam #2 Bring calculator and pencil For Monday January 12

Read 18.1-18.5, 18.8-18.9 Homework Ch 18, P: 3, 4, 26, 27

PAL #13 Capacitors 0.005 C stored on capacitor at 1000 volts What is capacitance?

Q= CV C = Q/V = 0.005/1000 = 5X10-6 F = 5 F

Jury-rig a replacement out of metal foil and Teflon coating (k = 2.1, thickness = 0.01 mm). C = 0A/d A = Cd/0 = (5X10-6)(0.00001)/(2.1)(8.85X10-12) A = 2.69 m2

How can such a device be portable? Roll it up, making sure the foil won’t short

Electric Potential Chart

 

  sign of U sign of V sign of W naturally?

+ charge moves with E field    

       

+ charge moves against E field    

       

-charge moves with E field     

       

-charge moves against E field    

       

    

--

--

-

-+

++

+

++ Yes

Yes

No

No

When a charge +Q is placed at the corner of a square the potential at the center is 3 volts. What is the potential at the center if charges of +Q are placed on all corners of the square?

A) 0 VB) 3 VC) 9 VD) 12 VE) 24 V

If a positive charge moves with the field,

A) PE increases, V decreases, Work positiveB) PE increases, V decreases, Work negativeC) PE increases, V increases, Work negativeD) PE decreases, V increases, Work positiveE) PE decreases, V decreases, Work positive

If a positive charge moves against the field,

A) PE increases, V decreases, Work positiveB) PE increases, V decreases, Work negativeC) PE increases, V increases, Work negativeD) PE decreases, V increases, Work positiveE) PE decreases, V decreases, Work positive

If a negative charge moves with the field,

A) PE increases, V decreases, Work positiveB) PE increases, V decreases, Work negativeC) PE increases, V increases, Work negativeD) PE decreases, V increases, Work positiveE) PE decreases, V decreases, Work positive

If a negative charge moves against the field,

A) PE increases, V decreases, Work positiveB) PE increases, V decreases, Work negativeC) PE increases, V increases, Work negativeD) PE decreases, V increases, Work positiveE) PE decreases, V decreases, Work positive

If a charged particle moves along an equipotential line (assuming no other forces),

A) Its potential energy does not change

B) No work is doneC) Its kinetic energy does not changeD) Its velocity does not changeE) All of the above