phys155-2012-02_handout.pdf

1

„Introduction to Electricity and Magnetism“

Dr. Li Chen- Copyright @Dr. Sven Achenbach, and Dr. Eric Salt -

University of SaskatchewanUndergraduate Course

Phys 155

Part 1, Topic 2 Electric Fields

Phys155 1-2: Electric Fields 2

Topic 2: Electric Fields

Introductory Remarks

• topic 2 deals with how electric fields are used to determine forces and work done

• it is a general introduction & link to your high school physics education,

not covered by our text book (Cutnell & Johnson)

• topic does not cover how electric fields are createdrefer to subsequent topic 3,

which is covered by the text book, and also develops equations to give exact forces for a certain electric field

a few definitions from topic 2 will be repeated in topic 3

2


Outline

slide #

particles of matter 4

electric fields 7

energy contours (equipotential surfaces) 11

energy stored in electric fields 16

electric potential (voltage) 18

relationship between E and V 24

electron volt 27


Particles of Matter

Fundamental Particles

• 3 fundamental particles of an atom

- electron

- proton

- neutron

• they have intrinsic properties of

- mass

- charge

3


Particles of Matter

Charge

• 2 types of charge

- negative (charge intrinsic to an electron)

- positive (charge intrinsic to a proton)

• base unit of charge is Coulomb C

this is the charge on about 6.2421018 electrons or protons

• 1 electron or 1 proton carry the smallest amounts of (neg. or pos.) net charge

they have the same magnitude (just the sign differs)

- charge on 1 electron is denoted –e or e-

- charge on 1 proton is denoted e or +e or e+

CCe 19

1810602.1

10242.6

1


Particles of Matter

Intrinsic Properties

particle charge [C] mass [g] radius [m]

electron -1.60210-19 9.0910-28 210-15

proton +1.60210-19 1.67310-24 210-15

neutron none 1.67510-24 210-15

4


particles of matter

electric fields

energy contours (equipotential surfaces)

energy stored in electric fields

electric potential (voltage)

relationship between E and V

electron volt


Electric Fields

Force

• an electric field is a force field

• the force acts on the intrinsic property of charge

• the force exerted by the field

is proportional to the excess charge (net charge) on the (test) object(an object has excess charge if it has more (or fewer) electrons than protons)

• the force [in Newtons N] per unit charge [in Coulombs C] is denoted E [in units of N/C]

• the force lines of a map of an electric field are called E lines or electric field lines

• the arrows on the field lines indicate the direction of force

the field exerts on a positive charge

5


A particle located at point A

has an excess (net) charge of +19 C.

What is the magnitude of the force on that particle?

Is the direction of the force

down & to the left or up & to the right?

Electric Fields

Example 1


Electric Fields

Notation

timesunit vector in x-direction

atpoint(x,y,z)

value of Ein direction of x-axis

• E is a 3-dimensional vector [in units N/C]

that is a function of position

• in general, E at a point (x,y,z) is expressed as

or without giving the coordinates for the point

• E (x,y,z) = |E (x,y,z)| is called the electric field strength at point (x,y,z)

• the field strength at a point A labeled on a map is often written as E or EA

kzyxEjzyxEizyxEzyxE zyxˆ,,ˆ,,ˆ,,,,

kEjEiEE zyxˆˆˆ

6


particles of matter

electric fields





electron volt


Energy Contours (Equipotential Surfaces)

of an Electric Field

• energy contours on a map of an electric field are called equipotential surfaces (lines)equi... from latin: aequus: same (or here: constant)

along an equipotential surface (line),

the value remains the same / constant

from equipotential surface (line) to surface (line)

the value changes

• value associated with equipotential surfaces (lines) is called

(electric potential energy) or shorter & better ‚electric potential‘ or ,potential‘

[in units Joules/Coulombs J/C]

3D 2D

7


1) What is the electric potential of point A?

2) What is the electric potential of point B?

3) What is the electric potential of

point A with respect to point B?

4) How much work is required to move

a positively charged particle

with an excess charge of +23 C

from point A to point B?


a positively charged particle

with a net charge of +11 C

from point D to point A?


Example 2


1) What is the average force per unit charge

exerted by the field on a charged object

moved from A to B

along the electric field line that links them?

The straight line distance from A to B

is measured to be 0.4 m.

2) What is the average tangential component of the force exerted by the field

on a charged object if the object is moved along curve S from point C to D,

and curve S is 2 m long?


Example 3

8



Example 3

1) What is the average force per unit charge

exerted by the field on a charged object

moved from A to B

along the electric field line that links them?

The straight line distance from A to B

is measured to be 0.4 m.

Note:

result for assumption of positively charged object

this negative value (-2.5 N/C) states that the mover exerts a force

in opposite direction of the movement (definition of work)

the force exerted by the mover is opposite to the force exerted by the field (upstream)

force exerted by the field is +2.5 N/C in the direction of the motion

(which is in the direction of the field lines )


particles of matter

electric fields





electron volt

9


Energy stored in Electric Fields

Moving Charges

• whenever a mover does positive work

by moving charge in space (in an electric field),

the energy of the electric field increases

e.g.- moving a pos. charge from lower to higher potential pos. work done energy of electric field increases

- neg. lower to higher work given off decreases

- pos. higher to lower work given off decreases

- neg. higher to lower pos. work done increases


particles of matter

electric fields





electron volt

10


Electric Potential (Voltage)

of an Electric Field

• knowing the electric potential between 2 points in an electric circuit

is key to the analysis of that circuit

• the electric potential is always measured between 2 points

• the variable (symbol) for the electric potential is VNote: sometimes, the variable is referred to as U instead of V)

• the variable VAB is used to represent the electric potential between points B and A,

referred to as “electric potential (or voltage) at point A with respect to point B“

by definition, the work W

required to move an object with a net charge Q from point B to point A is

• unit of the electric potential (derived from Joules/Coulombs J/C) is a Volt Vthis is why the electric potential is also referred to as voltage

• Note: the symbol V is used for both, variable representing the electric potential and its abbreviated unit Volts.

Sometimes, the variable is written in italic font or replaced by U. Otherwise, they are distinguished by context.

Q

WVAB


1) An object with a net positive charge of 7 C is moved from point A to point B.

To do this, the mover does 21 J of work .

What is the electric potential at point B with respect to point A (i.e., what is VBA)?

2) What is the potential energy of an object at point B with respect to point A

if that object is positively charged with +2 C of charge?


Example 4

11


Points G and H are 2 points in space where an electric field is present.

VHG = 10 V.

How much work is required to move +19 C of charge from point G to H ?


Example 5


Points G and H are 2 points in space where an electric field is present.

VHG = 10 V.

How much work is required to move -19 C of charge from point G to H ?


Example 6

12


1) What is the direction of the electric field?

2) What are VAB and VBA?

3) What is VCD?


-29 C of charge from point D to point A?

5) What is the strength of the electric field

at H if dx = 1 m?


Example 7


particles of matter

electric fields





electron volt

13


• suppose points A and B are on the same electric field line and are a distance x apart

• to move a particle with excess charge Q from points B to A,

the mover must exert an average force Fave in the direction of the movement

• with the general definition of work (or energy) W = F x,

and work W to be done by a mover to move the particle from B to A (Fave is positive, if its direction is from B to A)

• division by Q:

• the mover exerts the force Fave against the field force (and the related electric field Eave)with field E = force per unit charge [N/C] as defined earlier, and with the neg. sign as above,

Relationship between E and V

Moving a Charge in a Field

x

WFave

x

W

QF

Qave

11

xQ

W

Q

Fave

1

x

V

Q

F ABave

aveave EQ

F

x

VE ABave

C

N

mC

Nm

mCJ

m

VNote: equation justifies that units of electric field N/C are also V/m:


• for now, denote VAB as V

electric field strength of the electric field was derived to be

• now, decrease x:

field strength will be the same at points A and B and all points inbetween:

E remains constant for extremely small distances x → dx

electric field strength is given by

Relationship between E and V

x → dx

dx

dV

x

V

x

VEave

dx

dVE

14


particles of matter

electric fields





electron volt


Electron Volt

Definition

• an electron volt is denoted eV

• magnitude of work (or energy) required

to move the charge of one electron or proton (e = 1.60210-19 C)

between 2 points that have a difference in electric potential of V = 1 V

1 eV = (1 V) (e)

= (1 V) (1.60210-19 C)

= 1.60210-19 VC

= 1.60210-19 J

• reciprocally, using the definition of eV, the charge on 1 proton is

e = (1 eV) / (1 V) = 1 e

15


An electron is moved from point A to point B in an electric field where VBA = -7 V.

1) Is the work done by the mover positive or negative?

2) How much energy (in units of Joules) is transfered from the mover to the field?

3) How much energy (in units of eV) is transfered from the mover to the field?

Electron Volt

Example 8

phys155-2012-02_handout.pdf

Documents