Ch 17 1

Chapter 17

Electric Potential, Electric Energy and Capacitance

© 2002, B.J. Lieb

Giancoli, PHYSICS,5/E © 1998. Electronically reproduced by permission of Pearson Education, Inc., Upper Saddle River, New Jersey

Ch 17 2

Review of Work and Energy

Electric potential is based on the concept of work and energy.

•Work = (force) (distance) (cos )•Units are J (joules) 1 J = N m

•Potential Energy is energy of position such as the energy stored in a stretched spring or a roller coaster at the top of the first hill

•You have to do work to move a positive charge in an electric field to point a, so that charge has electrical potential energy (Pea)

•If you release the charge it will “fall” away from the other charge thus gaining kinetic energy KE = ½ m v2

Ch 17 3

Electric Potential

• Electric potential Va is potential energy per unit charge

++++++++++++++

______________

+ +b a

q

PEV a a

•Often “potential” is used instead of electric potential

•Unit is a volt (V) which is a joule/coulomb

• 1 V = 1 J / C

Point b has a higher electric potential than a and thus a positive particle at a has more potential energy than at b.

Ch 17 4

Potential Difference

•The difference in potential energy between two points a and b is the work done in moving a charge from one point to the other Wba ( assuming the charge is moved slowly so there in no KE.

•The same is true for electric potential.

q

WVVV ba

baab

q

WV ba

ab

Ch 17 5

Potential Energy Difference

• Since electric potential is potential energy per unit charge, we can find the change in potential energy

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______________

+ +b aExample: The two

parallel plates shown are connected to a 9 V battery. If the charge is +4 C, then the potential PE = (9V) (4 C)= 36 J

•If the charge were released at point b it would “fall” to a and gain 36 J of kinetic energy if there was no friction.

baab qVPEPEPE

Ch 17 6

Electric Potential and Electric Field

• Consider the uniform electric field between parallel plates

• Ignoring signs the work done by the field to move the charge from b to a is W= q Vba

• Since the E field is uniform, we can also calculate W from W = F d = q E d

• We can combine these two equations to give Vba

= E d

• This equation is usually written

++++++++++++++

______________

+ +b a

d

VE ba

Ch 17 7

Example 1

Ch 17 8

Equipotential Lines

• A 9 volt battery is connected to the parallel plates

• Thus the positive plate is at a potential of 9 V and the negative plate is a 0 V.

• The green lines are called equipotential lines because every point on the line is at the same electrical potential

• Notice how the voltage drops as you go from the 9 V plate, which is also an equipotential to the negative plate at 0 V

• The green lines are actually surfaces in 3D

• The equipotentials are always perpendicular to the electric field lines.

++++++++++++++

______________

9 volts

7.75 V2.25 V

4.5 V

Ch 17 9

Equipotential Lines of Two Point Charges

Ch 17 10

The Capacitor

• What would happen to the charged parallel plates if the battery were disconnected?

• Answer: Nothing: the + and – charges are attracted to each other, so they would remain.

• Notice that this is a charge storage device.

• It also stores energy.

• The potential difference or voltage V will remain constant

• This device is called a capacitor and it is often used in electrical circuits.

• Often the plates are made of a thin foil with a thin insulator between the plates. This can then be rolled up to form a very compact device

++++++++++++++

______________

9 volts

Ch 17 11

The Electron Volt

•Many devices accelerate electrons and protons through a given potential difference

•Because all charges are e or multiples of e, a special unit of energy has been created called the electron volt

•Definition: An electron volt (eV) is the energy gained or lost when a particle of charge e moves through a potential difference of 1 V.

• 1 eV = q V = (1.60x10-19 C)( 1.0V) = 1.60x10-19 J

•Example: An electron in a TV tube is accelerated through a potential difference of 25,000 V. What is the kinetic energy of the electron?Answer: KE = 25,000 eVKE = (25,000 eV) (1.6x10-19 J/eV) = 4.0x10-15 J

Ch 17 12

Electric Potential due to Point Charges

•To derive an expression for the electric potential of a point charge +Q, we calculate the work done per charge to move a test charge from infinity to a point that is a distance r from Q.•This derivation requires calculus because the electric repulsion increases as the test charge moves closer.•The result of this derivation is:

r

QkV

r

V

Ch 17 13

Example 2

Ch 17 14

Capacitor Equations I

++++++++++++++

______________

We will now derive several equations that describe the capacitor.

CVQ

•The unit of capacitance is the farad (F).

•Q is the charge on one plate (and there is an equal but opposite charge on the other plate) and V is the voltage.

• 1 F = 1 C / V

•We refer to C as the capacitance.

•Most capacitors are F or smaller

Ch 17 15

Capacitor Equations II

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______________

Another not-derived equation allows us to calculate the capacitance of a particular parallel plate.

C = 0 (A/d)

Where A is the area of the plates, d is the distance between them and 0 is called the permittivity of free space.

0 = 8.85 x 10 –12 C2/Nm2

The symbol of the capacitor used in circuit drawings is:

Ch 17 16

Dielectrics

Most capacitors have an dielectic material between the plates that

•Increases capacitance

•Allows higher voltages

•Maintains distance d

•The formula for a capacitor with a dielectric is (this is the formula to remember).

C = K 0 ( A / d )

where K is called the dielectric constant.

Dielectric Constants (20 degrees C)

Vacuum 1.0000

Air 1.0006

Vinyl (plastic) 2.8-4.5

Mica 7

Water 80

Ch 17 17

How Dielectrics Work

++++++++

________

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +- +

- +

•The molecules in dielectrics become polar which means that the electrons tend to be located closer to the positive plate as shown below.

•A test charge inside the dielectric feels a E field reduced by 1 / K and thus a smaller V. 0

00

KCV

QK

KV

Q

V

QC

Ch 17 18

Energy Storage in a CapacitorA battery must do work to move electrons from one plate to the other. The work done to move a small charge q across a voltage V is W = V q. As the charge increases, V increases so the work to bring q increases. Using calculus we find that the energy (U) stored on a capacitor is given by:

QVU2

1

Ch 17 19

Example 3

Ch 17 20

Cathode Ray Tube (CRT)

•Electrons are ejected from heated metal called cathode

•Then accelerated through potential difference of as much as 25,000 V

•Electron beam is then bent by horizontal and vertical electric fields created by the horizontal and vertical deflection plates.

•Electron beam then strikes fluorescent screen

•Points on screen fluoresce in different colors

•Electronics attached to deflection plates cause beam to paint a picture on screen

•Picture made with 525 horizontal lines

•Picture redrawn at 30 Hz