Welcome to Physics 152 © Hyde-Wright, ODU © Walker, Prentice Hall, 2007.

Welcome to Physics 152

©Hyde-Wright, ODU

© Walker, Prentice Hall, 2007

Walker, Chapter 19 2

Topics to be covered

• Electricity and Magnetism (Chapters 19-23)

• Light and Optics (Chapters 25-28)

• Modern Physics (Chapter 29-32)


Chapter 19 Electric Charges, Forces, and Fields

Fundamental Forces in Physics• Gravity • Electromagnetism • Weak Interaction • Strong Interaction

All of physics is based on these four forces


Energy in our World

• Nuclear Fusion in sun E=mc2

H H H H He + Energy Thermal Energy at surface converted to visible

light energy

• Light Energy Chemical Energy (photosynthesis)• Plants Fossil Fuels

Fuel for cars (motion) Fuel for power plants

• Plants Food Energy for thought, motion of muscles, etc...

Fusion

Radiation


Electrostatic Phenomena

• Rubbing things makes an electrostatic charge


Electrical ChargeEffect of Electric charge have been known since ~600 B.C.Greeks experiment: amber rubbed against fur - charge

(Greek word for amber is elektron.)

Glass rubbed against paper towel + charge

The SI unit of electrical charge is the Coulomb (C ).


The Structure of an Atom

The atom consists of a positively charged nucleus, orbited by negatively charged electrons. The nucleus contains protons (positive) and neutrons (neutral).


The ElectronOne of the fundamental particles found in nature is the

electron.

• The electron mass is 9.11 10-31 kg.• The electron charge (-e) is -1.6 10-19 C.

The symbol e is the magnitude of the electron’s charge


The Proton

The proton is not a fundamental particle.

The proton mass is 1.67 10-27 kg.

• The proton is 2000 times heavier than the electron, so the vast majority of an atom’s mass resides in the nucleus.

• The proton charge (+e) is +1.6 10-19 C.

• The proton charge and electron charge are known to be equal

and opposite.


• An object may contain both positive and negative charges. If the object possesses a net charge it is said to be charged. If the object possesses no net charge it is said to be neutral.

• An atom is normally neutral, because it possesses an equal number of electrons and protons. However, if one or more electrons are removed from or added to an atom, an ion is formed, which is charged.

• Charge is always conserved: charge may be transferred but it is never created or destroyed. However, charges can be created and destroyed in

positive and negative pairs, so that the net charge in the universe does not change.


Two charged objects will exert forces on one another.• Unlike charges attract one another.

• Like charges repel one another.

• The force decreases with the square of the distance between the charges

Electrical Forces

+

++


Polarization

An object is polarized when its charges are rearranged so that there is a net charge separation. Charged objects can be attracted to neutral objects because of polarization.

neutral & polarized

charged


Insulators and Conductors

Materials are classified by how easily charged particles can “flow” through them.

• If charges flow freely, the material is a conductor (metals, for example)

• If charges are unable to move freely, the material is an insulator (glass, for example)

• Some materials have properties in between insulators and conductors, these are called semiconductors.


Charge Transfer

Charge is usually transferred because electrons move from one place to another.But sometimes the flow of both positively or negatively charged ions (atoms or molecules) is important (cells, batteries…).

The earth can be viewed as an infinite (conducting) reservoir of electrons. An object in electrical contact with the earth is said to be grounded.


Coulomb’s LawThe magnitude of the force between two point objects

separated by a distance r with charges q1 and q2 is given by Coulomb’s Law:

where k = 8.99… 109 Nm2/C2

The direction of the force on one charge is either toward (negative) or away (positive) from the other charge.

221

r

qqkF

q1 and q2 are the values (+ or ) of the two charges


Force: vector, magnitude, component

• Magnitude (strictly positive)

221 ||||

||r

qqkF


12 1 2

21 2 1

21 12

Force on charge from charge

Force on charge from charge

: Newton's Third Law: Action-Reaction

F q q

F q q

F - F

12F 21F1q 2q

Force: vector, magnitude, component

• Magnitude (strictly positive)221 ||||

||r

qqkF

- +


Walker Problem 14, pg. 657Given that q = +12 C and d = 16 cm, (a) find the direction

and magnitude of the net electrostatic force exerted on the point charge q2. (b) How would your answers to part (a) change if the distance d were tripled?



b) Tripling the separations:


Multiple Charges

• If there are more than two charges present, the net force on any one charge is given by the vector sum of the forces on that charge from all surrounding charges. This is an example of the Principle of Superposition.

+

+

What is the direction of the net force on each charge (roughly)?


Walker Problem 20, pg. 658

Find the direction and magnitude of the net electrostatic force exerted on the point charge q2 in the Figure. Let q = +1.8 C and d = 47 cm.



Electric Field• If a test charge q0 experiences a force F at a given location r,

the magnitude of the electric field at that location is defined by

• The electric field can also be thought of as a disturbance in space caused by nearby charges.

• The electrostatic force experienced by a charge is the interaction between the charge and the electric field at that position.

• The SI units of electric field are Newtons/Coulomb = N/C

0

FE

q


Electric Force F(r) from charge Q acting on a test charge q0 at various locations r : F=kQq0/r2

Electric Field E(r)= F/ q0

Q

q0


Electric Field E(r) from charge Q at various locations r: E=kQ/r2

Q

r


Electric Field Direction

The direction of the electric field is defined to be the direction of the force that would be experienced if the test charge is positive. Because the field has a direction, it must be a vector.

+

q0 q0

E

E


Electric Field (cont.)The electric field is the force per charge at a given

location. If you know the electric field, then the force on a charge can easily be found using

F = qE

Example: A charge q of +8 C experiences a uniform electric field of 1000 N/C to the right. (a) What is the force on the charge? (b) What would the force be if the charge were –8 C?

Note: In problems like this we do not need to know what charges created the electric field. E = 1000 N/C

q


Electric Field of a Point Charge

From Coulomb’s Law, the magnitude of the force experienced by a test charge q0 a distance r from a charge q is

.20

r

qqkF

.2r

qkE

Since the definition of the electric field is

,0q

FE

the magnitude of the electric field from a point charge is given by


Walker Problem 28, pg. 642

What is the magnitude of the electric field produced by a charge of magnitude 10.0 C at a distance of (a) 1.00 m and (b) 2.00 m?

2r

QkE

k = 8.99 ·109 N m2/C2


SuperpositionJust like with forces, electric fields must be

added as vectors. The electric field from several charges is the vector sum of the electric field from each charge.

Example: Consider two identical negative charges as shown. At which lettered point is the magnitude of the electric field greatest? Least?

a cb


Walker Problem 76, pg. 661An object of mass m = 3.7 g and charge q = +44 C is

attached to a string and placed in a uniform electric field that is inclined at an angle of 30.0° with the horizontal. The object is in static equilibrium when the string is horizontal. Find (a) the magnitude of the electric field and (b) the tension in the string.



Electric Field LinesIn order to visualize the electric field in space it is convenient

to draw Electric field-lines (see Fig. 19-13). The field lines are directional [curved] lines that everywhere point in the direction of the electric field at that point.

+ +

Dipole


Field Line Properties

• The electric field is tangent to the field line at any point in space.

• The strength of the electric field is proportional to the density of field lines.

• The field lines always begin on positive charges or at infinity and end on negative charges or at infinity.

• No two field lines can ever cross.• The number of field lines leaving a positive charge or

approaching a negative charge is proportional to the magnitude of the charge.


Electric Field Lines

Note that twice as many field lines originate from the +2q charge than the +q or –q charges.


1. The net charge inside the grey ellipse is:

a) Positive

b) Zero

c) Negative

Hint: Are there more Electric Field lines entering, or leaving the gray ellipse, or is it equal?


2. The net charge inside the grey ellipse is:

a) Positive

b) Zero

c) Negative

Hint: Are there more Electric Field lines entering, or leaving the gray ellipse, or is it equal?


Electrostatic Equilibrium

Recall that charges within a conductor are free to move around easily.

If the charges within a conductor are not in motion, then the system is said to be in electrostatic equilibrium.


Properties of Electrostatic Equilibrium

• In the presence of electrostatic forces, the charges on the conductor move around until the following static conditions are achieved: The electric field is zero everywhere inside a conductor. The excess charge on a conductor resides entirely on its

surfaces. The electric field just outside a charged conductor is

perpendicular to its surface.

• On irregularly shaped objects, the charge accumulates at sharp points, and the electric field is most intense at sharp points.


Electric FluxWe define electric flux as

the product of the surface area A times the component Ecos of the electric field perpendicular to the surface.

In general, = EAcos

aEA

b = 0

(c) = EAcos

is the angle between the electric field and the line perpendicular to the surface.


Gauss’s LawConsider an arbitrary (imaginary) closed surface (called a

Gaussian surface) enclosing a total charge q. The electric flux through the surface is

0q

22124

10 m/NC1085.8

k

This integral property is a consequence of the 1/r2 Coulomb Law, and is valid for any irregular surface, no matter how complicated the electric field produced by internal or external charges.


ExampleThree point charges are arranged as shown. q1 = +4 C, q2

= -6 C and q3 = -4 C. Find the electric flux through the three Gaussian surfaces labeled a, b and c.

q1

q3

q2

acb


• Two charges Q1 and Q2 are separated by a distance of 0.010 m. The Electrostatic force of Q1 on Q2 is 2.0e-5 N.

• At what distance of separation between Q1 and Q2 would the force be 1.0e-5N? a) 0.02 m b) 0.014 m c) 0.01 m d) 0.007m e) 0.005 m

Welcome to Physics 152 © Hyde-Wright, ODU © Walker, Prentice Hall, 2007.

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