Electrical Energy and Capacitance Concept of potential difference and

potential Potential and potential energy for

point charges Potentials and charged conductors

Equipotential surfaces to capacitance

Clicker question I If the distance between two negative

charges is decreased by a factor of 3, the resultant force between the two charges changes by what factor?

A. Decreases to 1/9B. Decreases to 1/3C. Increases by 9D. Increases by 3

A question A suspended object A is attracted to a

neutral wall. It is also attracted to a positively charged object B. Which of the following is true?

A. The object A is unchargedB. It has a positive chargeC. It has a negative chargeD. It may be either charged positively or

negativelyE. It may be either charged or uncharged

Polarization Forces

A charge near a neutral object can move other charges. Like charges move away and unlike move front. All resulting in a net attraction.

A weak force

-q

-Q

-Q

-Q

+Q

+Q

+Q

Chapter 16:Lecture IIWe have talked about Electric Potentials.

V = U/q =

Scalar (not a vector)Adds like numbers.

i i

i

r

qk

||

-q1

q2

q3

-q4

4

4

3

3

2

2

1

1

r

q

r

q

r

q

r

qkV

F

E

U

V

qFE /

qUV /

x

UFx

The Electron Volt The electron volt (eV) is defined as the

energy that an electron gains when accelerated through a potential difference of 1 V Electrons in normal atoms have energies of

10’s of eV Excited electrons have energies of 1000’s of

eV High energy gamma rays have energies of

millions of eV 1 eV = 1.6 x 10-19 J

Equipotential Surfaces An equipotential surface is a

surface on which all points are at the same potential No work is required to move a charge

at a constant speed on an equipotential surface

The electric field at every point on an equipotential surface is perpendicular to the surface

Equipotentials and Electric Fields Lines – Positive Charge

The equipotentials for a point charge are a family of spheres centered on the point charge

The field lines are perpendicular to the electric potential at all points

Equipotentials and Electric Fields Lines – Dipole Equipotential lines

are shown in blue Electric field lines

are shown in gold The field lines are

perpendicular to the equipotential lines at all points

Application – Electrostatic Precipitator It is used to remove

particulate matter from combustion gases

Reduces air pollution Can eliminate

approximately 90% by mass of the ash and dust from smoke

Recovers metal oxides from the stack

Application – Electrostatic Air Cleaner Used in homes to reduce the

discomfort of allergy sufferers It uses many of the same

principles as the electrostatic precipitator

Application – Xerographic Copiers The process of xerography is used

for making photocopies Uses photoconductive materials

A photoconductive material is a poor conductor of electricity in the dark but becomes a good electric conductor when exposed to light

The Xerographic Process

Application – Laser Printer The steps for producing a document on

a laser printer is similar to the steps in the xerographic process Steps a, c, and d are the same The major difference is the way the image

forms on the selenium-coated drum A rotating mirror inside the printer causes the

beam of the laser to sweep across the selenium-coated drum

The electrical signals form the desired letter in positive charges on the selenium-coated drum

Toner is applied and the process continues as in the xerographic process

Capacitance A capacitor is a device used in a

variety of electric circuits The capacitance, C, of a capacitor

is defined as the ratio of the magnitude of the charge on either conductor (plate) to the magnitude of the potential difference between the conductors (plates)

Capacitance, cont

Units: Farad (F) 1 F = 1 C / V A Farad is very large

Often will see µF or pF

V is the potential difference across a circuit element or device

V represents the actual potential due to a given charge at a given location

V

QC

Parallel-Plate Capacitor The capacitance of a device

depends on the geometric arrangement of the conductors

For a parallel-plate capacitor whose plates are separated by air:

d

AC o

Parallel-Plate Capacitor, Example

The capacitor consists of two parallel plates

Each have area A They are separated by a

distance d The plates carry equal and

opposite charges When connected to the

battery, charge is pulled off one plate and transferred to the other plate

The transfer stops when DVcap = DVbattery

Electric Field in a Parallel-Plate Capacitor

The electric field between the plates is uniform

Near the center Nonuniform near the

edges The field may be

taken as constant throughout the region between the plates