BELLRINGER

Compare and explain in

complete sentences and formulas

what is the unit for nuclear force.

Homework due tomorrow

WHAT IS THE LAW OF

CONSERVATION OF ENERGY?

GIVE EXAMPLES.

There are Four Fundamental Forces:

1) The Electromagnetic Force

3) The Strong Nuclear Force

4) The Weak Nuclear Force

(We’ll study it this term)

These act over a very small range

These are responsible for

all we see accelerate 2) The Gravitational Force

The Unification of Forces

Physicists would love to be able to show someday that the four fundamental forces are actually the result of one single force that was present

when our universe began.

Superstring Theory is an interesting and promising possibility in this quest:

Web Links: Superstring Theory The Elegant Universe The Fabric of the Cosmos

Recent Physics Discovery!

Now let’s review the gravitational force…

Any two masses are attracted by equal and opposite gravitational forces:

m1 m2

r

F -F

Newton’s Universal Law of Gravitationwhere…… F G

m mr1 2

2

G=Universal Gravitation Constant = 6.67x10-11 Nm2/kg2

This is an Inverse-Square force Gravity is a very weak force

atom

If an atom has the same amount of + and - charge

Neutral (no net charge)

If it’s missing electrons

net + charge

If it has extra electrons

net - charge

silk

glass

(rub)

- --

(rub)

- --

+ + + +

fur

plastic- - - -

Web Links: Static DusterNew Carpet

Ex:

If you rub a balloon against your hair, which ends up with more electrons, the

balloon or your hair?

Opposites Charges Attract

Like Charges

Repel

Insulators (like plastic, rubber, pure water, and glass) will

not conduct away extra charge.

Conductors (such as metals, tap or salt

water, and the human body) are good at conducting away any extra

charge.Metal:

“free electrons”

Touching it with your hand will

discharge it

Use rubber gloves in the lab

Grounding

- - - -

The earth is a huge reservoir of positive and negative charge

+ +

+

+

++

+

+

+-

-

--

-

--

--

-

-

---

- Object is discharged or “grounded”

Induced Charge (Charging by Induction)

What happens when you bring a neutral metal

object near a positively charged object?

+

+

+

+

- - - -

What happens when you bring a neutral metal

object near a negatively charged object?

Web Links: Charging by Induction 1Charging by Induction 2

Electric Current

wire

- -- electrons

Current

Electric current is in the direction that positive charge

carriers “would” move

why? ask Ben Franklin

Current = Charge per Time

I

I q t Amperes (A) Coulombs (C) seconds (s)

SI units

q t

Remember, opposite charges attract:

and like charges repel:

q1 and q2 may

represent lots of extra or missing

electrons

How much force do q1 and q2 exert on each other?

Coulomb’s LawF electrostatic force k

q q

r1 2

2

k = electrostatic constant = 8.99 x 109 Nm2/C2

Web Link: Orbiting electron

Notes on Coulomb’s Law

1) It has the same form as the Law of Gravitation: Inverse-Square Force

2) But… (can you spot the most basic difference between these two laws?)

3) The electrostatic constant (k) in this law is derived from a more fundamental constant:

k1

4

00= permittivity of free space

= 8.85 x 10-12 C2/Nm2

4) Coulomb’s Law obeys the principle of superposition

Web Links: Coulomb force, Releasing a test charge

Ex:

+q +q-q

r r

What is the direction of the net force on the charge in the middle ?

What about the charge on the left?

What about the charge on the right?

Ex:

q1

q2

q3

.15 m

.10 m

73°

q1= +4.0 C

q2= -6.0 C

q3= -5.0 C

Find the net force on charge q1

Smallest possible amount of charge:

1 extra electron: q = -1.60 x 10-19 C

1 missing electron: q = +1.60 x 10-19 C

For any charge q:

q = ne , where n = 1, 2, 3, etc…

…

Charge is quantized Also:

Charge is conserved

= e = elementary

charge

Ex:

- +

electron proton

1.0 cm

Calculate both the gravitational force and the electrostatic force, and compare their magnitudes.

Electric Fields

Field – A set of values that defines a given property at every point in space

Temperature Field: Elevation Field:

Both of these examples are scalar fields

We need to look at a vector field

Wind

Notice that the wind vectors each have magnitude and direction

This is an example of a vector field

Here is an animated example: Wind Map

Electric Field (E) – A vector field surrounding a fixed, charged object that indicates the force on

a positive test charge (q0) placed nearby

Draw the Electric Field vector at the position of the test charge. Draw the Electric Field vectors at several other positions surrounding the fixed, charged object.

fixed, charged object

+

++ +

+ ++

+

+

+ +test charge

Web Link: Force Fields

EF

q0

The Electric Field is defined as the Force per unit Charge at that point

Notes on E-field

1) The E-field points in the direction of force on a positive test charge

2) If a negative charge were placed in the E-field, what do you suppose would happen?

3) The E-field is a property of the fixed charges only (it is independent of the test charge)

4) E-fields add as vectors

5) Given the E-field value at a certain point, we can calculate the force F on any charge q0 placed there:

EF

q0

F = q0E

Ex:

+

q = 2.0 C

(fixed charge)

+

q0 = 1.0 C (test charge)

a) Find the force on the test charge using Coulomb’s Law

b) Find the electric field at the position of the test charge

c) Could you have answered part b without knowing the value of the test charge?

.10 m

Ek q

r 2

Electric Field at a distance r from a point charge q

r

E = ?

q

+

Electric Field Lines -represent symmetric paths of a positive test charge

The number of lines is arbitrary, as long as they are symmetric

The density of lines represents the strength of the Electric field What would the Electric field lines look like if there was a negative charge at the center?

What do you think the Electric Field lines would look like for…

A charged, non-conducting sheet that is not infinite?

+

++ +

+ +

+

+

+

+

A large (), charged, non-conducting sheet?

+

++ +

+ ++

+

+

++

+

++ +

+ +

+

+

+

+

--

--

-

-

Two oppositely charged plates?

(called a parallel plate capacitor)

The Electric Field Lines for 2 Equal Charges:

The Electric Field Lines for 2 Opposite Charges (called an Electric Dipole):

Web Links: Electric Field Lines, Releasing a test charge

Charged Conductors

Any excess charge ends up on the surface of a conductor, independent of its shape

Why do you think this happens?

What happens to a neutral conductor placed in an external electric field?

“Shielding”

E = 0

At equilibrium, the Electric Field at any point within a

conducting material is zero.

Faraday Cage: an example of shielding

Consider two charged spheres, one having three times the charge of the other. Which force diagram correctly shows the magnitude and direction of the

electrostatic forces?

++

+++++

+

++

+++++

+

++

+++++

++

+++

+++

+

++

+++++

+

++

+++++

+a)

b)

c) f)

d)

e)

Recall…

Gravitational Potential Energy

or

Elastic Potential Energy

Now…

-+

+++++

+

++

+ +

Electric Potential Energy

(EPE)

Only Conservative Forces have an associated PE

Recall:

PEgrav = mg(h) = -(Work done by gravity)

Similarly:

EPE = -(Work done by electrostatic force)

++++ +++

+++ +

-

-

= - (Fcos)s

Force displacement

angle between F and s

EPE = -W = -(Fcos)s

Ex:

Uniform Electric Field

+proton

E = 4.0 N/C

a) Find the force on the proton.

b) Find the work done by that force as the proton moves 2.0 m.

c) Find the change in EPE as it moves 2.0 m.

d) Find the change in EPE if an electron were to move through the same displacement.

+

2.0 m

Work is Path Independent for conservative forces:

path 1

path 2

Work done by gravity on path 1 = Work done by gravity

on path 2

Ex: Electric Field

path 1

path 2

Work done by electrostatic force

on path 1 =

Work done by electrostatic force

on path 2

Ex: Gravity

EPE is a type of mechanical energy, like…

Kinetic Energy (KE) = ½ mv2

Rotational Kinetic Energy (KER) = ½ I2

Gravitational Potential Energy (PEgrav) = mgh

Elastic Potential Energy(PEelast) = ½ kx2

= Total Mechanical Energy (E)is conserved if there are no non-conservative forces present (ie friction).

+++

+

Ex:

Uniform Electric FieldE = 150 N/C

A proton released from rest into this electric field will be going how fast after traveling a distance of 1.0 m ?

+proton

Can you think of two different methods to use in solving this problem?

Do they yield the same answers?

+

1.0 m

In both previous examples, we saw that…

EPE q

E

q

2q

Twice the charge has twice the EPE

We would like to have a new quantity that describes the “Potential” at various points in the

electric field independent of the charges in it:

Electric Potential VEPEq0

= EPE per charge

Also called Potential or Voltage

SI Unit = J/C = 1 Volt

From the definition of Electric Potential, we can show that when a charge is moved from

one point to another in an electric field:

Work done by the Electric

Field= -

Charge that was moved

Difference in Potential between its old and

new positions

E1

2

W = -q0(V)

Let’s make sure that we understand the difference between Potential and Electric Potential

Energy:

V (in Volts) = Potential

a property of a certain position in an Electric Field with or without

charges placed there

E

-

EPE (in Joules) = Electric Potential Energy

a property of charges placed at a certain position in an external Electric Field +

- EWeb Link: EPE vs Potential

We now have a new SI unit for Electric Field:

Volts / meter

There is a force of 3 Newtons on each 1 Coulomb of charge in the field

The Potential changes by 3 Volts for every 1 meter of distance

We also have a new energy unit (not SI):

The electron-Volt (eV) amount of energy gained (or lost) when 1 electron

moves through a potential difference of 1 volt

E = 3 N/C = 3 V/m

Ex

-

1 V

Equipotential Surfaces adjacent points at the same electric potential

E-field Equipotential Surface

Web Link: Equipotential surfaces

Equipotential Surface

E-Field

Equipotential Surfaces are 3-dimensional:

Equipotential Surface

E-Field

Notes on Equipotential Surfaces

1) Equipotential surfaces are always perpendicular to Electric Field lines

Web Link: Electric Field Lines

2) If a charge moves on an equipotential surface, the work done by the Electric Field is zero:

+

s

F

Web Link: Equipotential surfaces

In the case of a Uniform Electric Field, it is especially easy to calculate the potential difference

between equipotential surfaces:

E

++++

-

-

-

-

Potential gets higher in this direction

Potential gets lower in this direction

E is in Volts/meter

E = V/s

V = E(s)

Ex:

.30 m

E = 5.0 V/m

Find the potential difference between the plates.

In the lab, we could use a Voltmeter to simply measure the potential difference:

This means there is a potential difference (V) of 12 Volts between the terminals of the battery

Calculating the Potential due to a Point Charge

q

r

What is the Potential at this point?

V kqr

k = electrostatic constant = 8.99 x 109 Nm2/C2

Notes:

1) Include the sign of q in your calculation! (+ or -)

3) The equation can also be used for a charged sphere:

+

++++ +

++

++

rV k

qr

Total charge

Distance from center

2) Potential Difference can also be calculated:

V = V2 – V1 k

qr

kqr2 1

Van de Graff generator

Ex:

-

electron

a) Starting at 1.0 nm from the electron and moving out to 5.0 nm from the electron, what is the change in potential ?

b) What is the electric potential energy (in eV) of a proton that is placed at a distance of 5.0 nm from this electron?

c) What is the electric potential energy (in eV) of another electron at a distance of 5.0 nm from this one?

Calculating the Potential due to Multiple Point Charges

+ +

What is the value of the Electric field directly between equal charges?

What about the value of the Electric Potential there?

Electric Potential is a scalar not a vector

V = V1 + V2 + V3 + … (an

algebraic sum, not a vector sum)

Ex:+q

+q

-q -qP

Find the potential V at point P due to the four charges.

dd

d

d

Web Link: Complex Electric Field

Capacitor a device that stores energy by

maintaining a separation between positive and negative charge

(Symbol: )

Circuit Board

Capacitor

Resistors

Parallel Plate Capacitor

--

+q

-q

This is called “charging a capacitor”

q = charge of the capacitor

V

V = potential difference of the capacitor

q and V are proportional:

q = C V

C = Capacitance (a fixed property of each capacitor)

SI unit = 1 Farad (F) = 1 Coulomb / Volt

Dielectrics electrically insulating materials

Capacitor without a dielectric

Capacitor with a dielectric

What happens to the Electric Field?

The Electric Field magnitude is less in a dielectric

How much less depends on the dielectric constant () of the material

Calculating the Capacitance (C) of a parallel plate capacitor

A

A = plate area

d

d = plate separation

= dielectric constant

CA

d 0

(0= 8.85 x 10-12 C2/Nm2)Notice:

Capacitance is independent of both charge and voltage

Adding a dielectric increases the Capacitance

Web Links: Capacitance Factors, Lightning

How much Energy is stored by a capacitor?

Energy = ½CV2

VoltageCapacitance

What’s the energy density in an Electric Field?

Energy DensityEnergyVolum e

E 1

2 02

* For any electric field

+q

d

-q +q

D

-q

Consider a parallel plate capacitor with charge q and plate separation d. Suppose the plates are pulled apart until they are separated by a greater distance D. The energy stored by the capacitor is now

1. greater than before

2. the same as before

3. less than before

Here’s a Web Link about a huge capacitor and

what can be done with all that stored energy:

Pulse Discharge Machine

Imagine a wire:

V

+-

E

Web Link: DC Electricity

Now imagine bending the same wire into a loop: +

-V

- - -

Battery or other emf source

emf – electromotive “force” – the potential difference between the terminals of an electric power source

-

-

-

Ex:

emf = 9 V

+

-+

The current arrow points with the “positive charge carriers”

current Iqt

Web Link: Conventional Current

Notes on Current:

1) Remember: charge is conserved

SI unit = Ampere(A) = 1 C/s

2) Current is a scalar, not a vector

3) There are two types of current:

DC (direct current) charge moves the same

direction at all times

AC (alternating current) charge motion alternates

back and forth

Web Link: AC vs. DC

I

+

Ex:

I

A DC current of 5.0 A flows through this wire:

How much charge flows past this point in 4.0 minutes?

Will the bird on the high voltage wire be shocked?

Resistance RVI

applied voltage

resulting current

SI unit: Ohm () = 1 V/A

(Resistor symbol: )

Resistor – a circuit component designed to provide a specific amount of resistance to current flow.

Web Link: Resistance

9 V1000

Ex:

Draw the circuit diagram, and calculate the current in this circuit.

Building Resistors

Resistance = R = a property of a given resistor (Ex: 20 , 400 , etc.)

Resistivity = = a property of a material used in making resistors

A

L

RLA

(: SI unit = ·m)

Ex: Aluminum Power Lines

Consider an aluminum power line with a cross sectional area of 4.9 x 10-4 m2 . Find the

resistance of 10.0 km of this wire.

Ex: Incandescent Light Bulb

120 V

I = 12.4 A

Tungsten wire radius .045 mm

What is the length of the tungsten wire inside the light bulb?

Web Link: Light bulb

V = I R( I V )

I

V

( I V )

Is it really a law ?“Ohm’s Law”

It works for resistors:

What about other devices?

Diode

I

V

Light Bulb

I

V

“Ohm’s Law” is not really

a Law!

( I V )

Power = P = IV

SI Unit = 1 Watt (W) = 1 J/s

Rate of energy transfer

If the device is a resistor:

P = I V

V=IR

= I2R

P = I V

I=V/R

= V2/R Energy dissipated by the resistor as thermal energy

Ex: Space Heater

1500 W Heater

120 V

Find:a) The resistance of the heaterb) The current through the heaterc) The amount of heat produced in 1 hour

…back to the difference between AC and DC:

Web Link: AC vs. DC

DC ( ) :

Voltage

time

Ex:

AC ( ) :

Voltage time

Ex:

V = V0 sin ( 2 f t )

Voltage amplitude frequency time

radians

So what does AC current look like?

Typical household

outlet:V0 = 170 V f = 60 Hz

Light bulb: Resistance R

IVR

V sin 2 f t

R0

= I0 = current amplitude

I = I0 sin ( 2 f t )

It

Ex: Alarm Clock

How many times a day does the current change direction?

V0 = 170 V f = 60 Hz

look familiar??

AC PowerP = I V = ?

II

2rm s0 V

V

2rm s0

peak values

These are the values that matter

P = Irms Vrms

P = (Irms)2 R

P = (Vrms)2 / R

Ex:

V0 = 170 V

What is the rms voltage?

Ex: Speaker

If the power rating of the speaker is 55 Watts, and its resistance is 4.0 ,

what is the peak voltage?

Heating element of resistance R

AC generator

Resistors in Series

R1 R2 RS = R1 + R2

(RS > R1 , R2)

Resistors in Parallel

R1

R2

1R

1R

1RP 1 2

(RP < R1 , R2)

R R

Consider two identical resistors wired in series. If there is an electric current through the combination, the current in the second resistor is

1. equal to the current through the first resistor.

2. half of the current through the first resistor.

3. smaller than, but not necessarily half of the current through the first resistor.

A

B

As more resistors are added to the parallel circuit shown here, the total resistance between points A and B

1. increases

2. remains the same

3. decreases

Ex:

For some holiday lights, if one bulb is bad, the whole string goes out. For others, one bulb can go out and the rest stay lighted. What is

the difference ?

Basic Circuit: RV I = V/RI

IR1

Series Circuit:

V

R2

Current (I) has the same value everywhere in the circuit

current is like a parade

VR1 + VR2 = VBattery

voltage is like money

RSV

I I = V/RS

RS = R1 + R2

RPV

I1

Parallel Circuit:

I2 R1V R2

I3

I1

?

I1 = I2 + I3

VBatt = VR1 = VR2

Web Link: Parallel Current

1R

1R

1RP 1 2

I1 = V/RP I2 = V/R1

I3 = V/R2

Ex:

416 V

4

What is the series resistance?

Calculate the current in this circuit.

16 V 4 4

What is the parallel resistance?

Calculate the current in all branches of this circuit.

47 V

28

Ex:

The current through the 47 resistor is .12 A Calculate the voltage V of the battery.

Ex:

V 47 28

The current through the 47 resistor is .12 A Calculate the current through the 28 resistor.

R1

V

R2

In a series circuit, the current is the

same through each resistor

R1V R2

In a parallel circuit, the voltage is the same across each resistor

Notice that the terminology will help us remember how to measure current and voltage

Measure the voltage across a resistor:

Measure the current through a resistor:

You must break the circuit to

measure current!

How to calculate the equivalent resistance for a group of resistors:

Ex:

Find the equivalent

resistance of this circuit:

Kirchoff’s Rules

I) The Junction Rule

The sum of the currents entering any junction is equal to the sum of the

currents leaving that junction.

Web Link: Kirchoff’s 1st Law

I1

I2

I3

I4

I1+ I2+ I3= I4

Ex:

II) The Loop Rule

The potential differences around any closed loop sum to zero.

Web Link: Kirchoff’s 2nd Law

I2

I1

I3+

-

+

-

+

-+

-

V = I R

VR1 = I2R1

VR2 = I2R2

VR3 = ?

+V - I2R1 - I2R2 = 0

This loop (clockwise): Write out the equations for this loop and the outer loop

Ex:

R1

VR2

R3

Here are the steps for applying Kirchoff’s Rules to solve for unknown currents and voltages in a circuit:

Step 1) Label all the different currents in the circuit I1, I2, I3, etc. (current direction is arbitrary)

Step 2) Apply the junction rule at each junction (one junction will yield redundant information)

Step 3) Indicate which end of each device is + and -

I+ -+-

Step 4) Apply the loop rule to each independent loop

Step 5) Solve the equations for the unknown quantities

Ex:

8.0 V V

3.0

4.0

5.0

Use Kirchoff’s rules to find

a) the remaining two currents in the circuit, and

b) the unknown voltage

Web Link: Building circuits

1.7 A

Capacitors in Circuits

CA

d 0A

d

Recall:C A

C 1/d

C1V C2

Capacitors in Parallel:

CP = C1 + C2

Capacitors in Series:

C1V

C2

1C

1C

1CS 1 2

Ex:

8.0 F 5 V

6.0 F

4.0 F

a) Find the total capacitance of the circuit

b) Find the total charge stored on the capacitors

Charging a Capacitor:Web Link: RC Circuit I

At t = 0: close the switchFirst instant: I = V0/RThen: I decreases as the capacitor fills with charge

Finally: I = 0, and Vcap = Vbattery = V0

Web Link: RC Circuit II

Charg

e o

n

cap

aci

tor

time

q0 = CV0

full capacitor charge

RC = time constant =

q q 1 e0

tRC

RC Circuits

Discharging a Capacitor:

At t = 0: close the switch

First instant: I = V0/R

Then: I decreases as the capacitor loses its charge

Finally: I = 0, and Vcap = 0

Web Link: RC Circuit I

The capacitor starts out fully charged to voltage V0

Charg

e o

n

cap

aci

tor

time

Web Link: RC Circuit II

q q e0

tRC

Magnetic Field (B) points from “North” to “South” poles

Recall: Electric Field (E) points from + to - charge

opposite poles attract like poles repel

Magnetic Field LinesB is tangent to the field

lines at any point

The density of the lines represents the

strength of the magnetic field

Web Links: Magnetic Field 3-D Magnetic Field

Facts about Magnetic Fields (B-fields)

1) North and South poles cannot be isolated

2) All B-fields are caused by moving electric charge

3) The Earth has a Magnetic Field:

Web Links: Northern Lights

4) B-fields exert a force on moving, charged particles:

Force is out of the screen

B + Force is into of the screen

+unaffected +unaffected

+

Magnetic Force = F = qvBsin

v = speed of charge

B = magnetic field

= angle between v and B

q = chargeWhat is the direction of this force?

Fingers point with vThen curl toward BThumb points with F

SI unit for B-field is a Tesla (T)

(F is in opposite direction for a negative charge)

Other unit: 1 Gauss = 10-4 T

Right Hand Rule (RHR) (For a positive charge)

B

v

F

Since it’s difficult to draw in 3-D, we’ll adopt the following symbols:

dots indicate a B-field out of the page

x x x x

x x x xx x x xx x x x

x’s indicate a B-field into the page

(hint: just think of arrows: )

Web Links: Charged particles in a Magnetic Field Deflection of a moving electron

In the following examples, is the charge + or - ?

x x x x

x x x x

x x x x

x x x x

?

??

Work done by the Magnetic Force

x x x x

x x x x

x x x x

x x x x+

v

s

s

s

F

F

F

Work = (Fcos)s = ?

The work done by the Magnetic Force is equal to _____

The speed of a charge in a Magnetic Field is ______

Circulating Charged Particle

When the charge moves perpendicular to the B-field,

we can show that:

radius rm vqB

period T2 mqB

frequency fqB

2 m

Web Link: Charge in 2 Magnetic Fields

What path does the charge follow if v is not perpendicular to B? Web Link: Helix

Ex:

-

An electron in a magnetic field moves at a speed of 1.3 x 106 m/s in a circle of radius .35 m. Find

the magnitude and direction of the magnetic field.

Crossed () Electric and Magnetic Fields

x x x x

x x x x

x

x

B

E

- v

As the electron enters the crossed fields:

The Electric Field deflects it in what direction?

The Magnetic Field deflects it in what direction?

If E and B are adjusted so that the electron continues in a straight line…

vEB

Web Links: Magnetism inside a TV, TV Screens

Another example of Magnetic and Electric fields working together: A Particle Accelerator

The Large Hadron Collider (LHC), on the border of France and Switzerland, has a circumference of 16.7

miles. It accelerates particles to near the speed of light, so that high energy collisions can be used to further study the structure of matter. (Web Link: LHC News)

What happens to a current-carrying wire in a B-field?

Remember: current is just moving charge

B

IL

What is the direction of force on this wire?

We can derive an equation for the

magnitude of this force…

F = I L B sin = angle between B and current

x x x x

x x x x

x x x x

x x x x

Ex:

x

x

x

x xx

B = .440 T

L

L = 62.0 cm

m = 13.0 g

Find the magnitude and direction of the current that must flow through the red bar in order to

remove the tension from the springs.

Make sure you don’t confuse these two

separate effects:

1) A Magnetic Field exerts a force on a Current

2) A Current produces its own Magnetic Field

r

Magnetic Field due to a long straight current:

I

BThumb points with IFingers curl with B

Right Hand Rule #2

The magnitude of B depends on the distance r

from the current:

BI

2 r0

0 = 4 x 10-7 Tm/A

permeability of free space

Weblink: Right Hand Rule

Ex:

If a wire carries a current of 480 A, how far from the wire will the magnetic field have a value of

5.0 x 10-5 T ?

(roughly the value of earth’s magnetic field)

Parallel Currents

I1 I2

B1 x

x

x

x

d

L

Current I1 produces a B-field

This B-field exerts a force on current I2

(and vice versa)

What is the direction of force on I2 due to I1 ? (hint: use both right hand rules)

What is the magnitude of force on I2 due to I1 ? (hint: use both equations)

Consider a circular current…

I

I

I

I

Bx

BB

B

B

B

B

and use RHR #2 to determine the direction of the magnetic field at the center of the loop:

BI

2R0

At the center of the loop:

Radius of loop

or

I I I

If there are many circular loops:

B NI

2R

0

N = number of loops

Web Link: Compass in loops of current

Magnetic Fields add as vectors

I

I

I

The straight section creates a B-fieldThe circular section creates a B-field

Do these fields add or

subtract?

I

I

I

At the center of the loop:

Do the B-fields add or subtract in this case?

Solenoid

x x x x x x x x x x x x

B

inside:

I

I

For a long, ideal solenoid: B = 0n I

n = turns/length

Web Link: Solenoid Factors

What are solenoids used for?

doorbells

Web Link: How doorbells work

car starters

electric door locks

Ex:

The solenoid has 100 turns. If a current of 23 A runs through it, what is the magnitude

of the magnetic field in its core?

20 cm

Toroid

Asteroids

In video games, what does it mean to play in a

“toroidal world”

Web Link: Asteroids

From above

B

Magnetic Flux () is related to the number of

magnetic field lines passing through a surface

B

NS

B

Web Link: Flux

Magnetic Flux = = B A cos

B = magnetic fieldA = surface area = angle between B and the

Normal to the surface

SI unit = 1 Weber = T·m2

Ex: square loop

2.0 mB = 5.0 x 10-4 T

b) Calculate the magnetic flux through the loop

c) What happens to the flux if the normal is rotated by 30° ?

a) What is the angle in this example?

d) What happens to the flux if the normal is rotated by 90° ?

Recall: An emf is anything that produces a voltage difference (and therefore causes current flow)

I

I

I

I

Bx

B

Recall: For a current loop, we can determine the direction of the B-field at its center:

Here’s a quicker way to do this:

Loop Right Hand Rule Fingers curl with I Thumb points with B

B

I

Faraday’s Law of Electromagnetic Induction

An emf is induced in a conducting loop whenever the magnetic flux () is changing.

em ft

Web Links: Induction, Faraday’s Experiment

Notes: 1) /t = rate of change of flux

2) Induced emf causes induced current in the loop

3) Induced current causes its own magnetic field

4) This new B-field direction opposes the change in the original one. This part is called Lenz’s Law.

Web Link: Lenz’s Law

5) If there are multiple loops:

em f Nt

(N = number of turns)

B

A

Here is a conducting loop in a magnetic field

Magnetic Flux = = B A cos

Can you think of 3 different ways to induce a current in this loop?

Ex:

NS

B

As the loop moves to the left, what is the direction of the current that is induced in it?

As loop moves left:

Ex:

x x x x

x x x x

x x x x

x x x x

As the loop is pulled and its area is decreased, what is the direction of the

current that is induced in it?

Web Link: Induced current

Notice in the previous examples:

If the magnetic flux is increasing, the induced B-field is in the opposite direction as the original B-field

B

If the magnetic flux is decreasing, the induced B-field is in the same direction as the original B-field

B

Web Link: Lenz’s Law

N S

Ex:

Find the direction of current in the loop when:

a) The magnet moves to the left

b) The loop moves to the left

c) Both the magnet and loop are stationary

B

Ex:

x x x x

x x x x

x x x x

x x x x

B = 2.0 T

20 cm

20 cm

The wire loop has a resistance of 20 m. If its area is reduced to zero in a time of .20 s, find the magnitude and direction of the induced current.

Finally…

why does it take so long for a magnet to fall through an aluminum pipe??

Web Link: Lenz’s Law Pipe

There are many familiar examples of induction

all around us…

Web Link: Generator

Generator

Web Link: Dynamic Microphone

Dynamic Microphone

Speakers

Web Link: How a speaker works

Electric Guitar

Web Link: Electric Guitar

Motional emf

speed v

conductor

What happens to the positive

charge on the conductor?

What about the negative charge?

Potential difference between the top and

bottom =

x x x x

x x x x

x x x x

x x x x

B

L

Motional emf = vBL

Ex: If the conducting bar is moved along conducting rails as shown below, we can see that there will

be a current in the direction indicated:

Could we have found the current direction using Lenz’s Law instead?

Near San Francisco, where the vertically

downward component of the earth’s magnetic field is 4.8 x 10-5 T, a car

is traveling forward at 25 m/s. An emf of 2.4 x

10-3 V is induced between the sides of

the car.

a) Which side of the car is positive, the driver’s or passenger’s?

b) What is the width of the car?

Circuits

DC voltage source

AC voltage source

Resistor

Capacitor

Inductor(Solenoid)

E-field inside

B-field inside

If N = number of turnsI = current = magnetic flux

Inductance = LN

I

SI unit = Henry(H) = Wb/A

The inductance (L) of a solenoid is not determined by the current or flux through it at a particular moment.

A

Recall:n = turns / length

L = 0 n2 A ℓ

Inductors store energy in their B-fields:

Energy stored in an inductor = ½ L I2

Energy DensityEnergyVolum e

B2

2

0

L is a fixed property of each inductor:

How do inductors behave in circuits?

BL

+ -

I I Constant B

very boring

Constant I

Changing I Changing B Changing

Induced emf

em f LIt

voltage across inductor

Opposes change in I

Since there is only one inductor, this is called

Self-Induction

When two inductors affect each other, it is called Mutual-Induction

+ -

1 2

I1

B1

2

N2 turns

If I1 changes

B1 changes

2 changes

emf2 induced in circuit 2

em f MIt21

MN

I2

1

2

Mutual Inductance =

Primary Circuit

Secondary Circuit

During a 72-ms interval, a change in the current in a primary coil occurs. This change leads to the appearance of a 6.0-mA current in a nearby

secondary coil The secondary coil is part of a circuit in which the resistance is 12 . The mutual

inductance between the two coils is 3.2 mH. What is the change in the primary current?

Recall : Power = I V

IV

IV

Current is reduced to minimize power loss

Voltage is reduced to household levels

How is the power line voltage raised and lowered?

Transformer Station

Transformer - increases (steps up) or decreases (steps down)

ac voltage using induction

Web Link: Faraday’s Transformer

Iron

generator

Primary Coil

Voltage VP

NP turns

Secondary Coil

Voltage Vs

NS turns

VV

NN

S

P

S

P

Transformer Equation

Web Link: Transformer

Transformer:

Ex:

?120 V 3.0 A

Find the output voltage and current.

Recall the difference between AC and DC:

Web Link: AC vs. DC

DC ( ) :

Voltage

time

Ex:

AC ( ) :

Voltage time

Ex:

V = V0 sin ( 2 f t )

Voltage amplitude frequency time

V0

-V0

Before we study AC circuits, let’s prepare by reviewing how the circuit components behave in a DC circuit:

I = V/RI

R

V CI

I = V/R at the first instant, then it decreases until I = 0

RV

At this point, the capacitor is fully charged, and acts like a break in the circuit

I

R

V L

Induced emf across L slows current increase until I = V/R

At this point the flux is no longer changing, and the inductor acts like a wire.

Resistor in an AC Circuit

V = V0sin(2ft) R

II

2rm s0

VV

2rm s0

IV

Rrm srm s

These are all average

valuesWhat about the

instantaneous values?

Web Link: AC Circuits

It

Vt

Voltage and Current are in phase in a purely

resistive circuit.

Capacitor in an AC Circuit

Acts like a resistor:

R = X1

2 f CC

Capacitive Reactance

SI unit = Ohms ()IVXrm s

rm s

C

What happens to XC when the frequency is very large ??

What happens to XC when the frequency is very small ??

CVrms f

Instantaneous Values for a Capacitor in an AC Circuit

Web Link: AC Circuits

V

t

I (q/t)

t

Capacitor is full here: q=0 Capacitor is charging

fastest when empty

Current leads Voltage by 90° in a purely

capacitive AC circuit

Power = I V one is maximum when the other is zero

Average Power ( P ) = 0 for a capacitor in an AC circuit

L

Inductor in an AC Circuit

Acts like a resistor:

R = X 2 f LL

Inductive Reactance

SI unit = Ohms ()I

VXrm srm s

L

What happens to XL when the frequency is very small ??

What happens to XL when the frequency is very large ??

Instantaneous Values for an Inductor in an AC Circuit

Web Link: AC CircuitsL

I

t

V (

I/t) t

I is not changing: V=0

I decreasing fastest: V is minimum

I increasing fastest: V is maximum

Current lags Voltage by 90° in a purely

inductive AC circuit

Power = I V one is maximum when the other is zero

Average Power ( P ) = 0 for an inductor in an AC circuit

Series RCL Circuits

Acts like a resistor:

R = Z R X X2L c

2

IVZrm srm s

Phase Angle between I & V = = tanX X

R1 L C

cos = power factor

Impedance ()

Average Power ( P ) = Irms Vrms cos

Ex:

16.0

4.10 F

5.30 mH

a) Find Irms

b) Find the voltage across each circuit element

c) Find the average power dissipated in the circuit

15.0 V 1350 Hz

Non-Series RCL Circuits

Vrms , f

a) Find Irms for a very large frequency

b) Find Irms for a very small frequency

I

I

Mass on a spring

Resonance in AC Circuits

Oscillating systems:

KE PE PE

AC Circuit

++++

- - - - B-fieldE-fieldWeb Link:

Electromagnetic Oscillating Circuit

LC This circuit has a natural frequency

f1

2 LC0

Resonant frequency for an RCL circuit(independent of R)

Ex: Tuning a Radio

Web Link: Radio Tuning

Electromagnetic Wave

Mutually perpendicular and oscillating Electric and Magnetic fields

Web Link: Electromagnetic Wave

Electromagnetic waves travel at the speed of light in a vacuum: c = 3.00 x 108 m/s

Electromagnetic waves are transverse waves

Recall these facts:

1) A changing B-field produces an E-field

2) A changing E-field produces a B-field-+

atom

E-field B-field E-field B-field

It could go on forever!

This is how to make an electromagnetic wave

Web Links: Propagation of an electromagnetic wave

Vibrating Charges

B

The Electromagnetic (e/m) Spectrum

c = f

speed of light frequency

wavelength Web Link: Wavelengths

Remember these constants?

0= permittivity of free space

0= permeability of free space

Fundamental constants of

nature

In 1865, Scottish physicist James Clerk Maxwell hypothesized electromagnetic waves and

calculated that they would have to travel at a specific speed in a vacuum:

1

0 oDo the calculation.

What do you get?

This is the measured speed of light! Electromagnetic Waves do exist,

and light must be one of them!

const. velocity

Our Reference Frame determines where and when we observe an event:

x

y

z

x

y

z

In both cases, the Reference Frame is at rest with respect to the observer

For each of the cases below, what path does the observer see the ball follow after he

throws it straight up?

on the ground

in a truck with constant velocity

in a truck with constant acceleration

Inertial Reference Frames (constant velocity)

Non-Inertial Reference Frame

Special Relativity Postulates

1) The laws of physics are the same in any inertial reference frame.

2) The speed of light in a vacuum (c) has the same value when measured in any inertial reference frame,

even if the light source is moving relative to it.

speed of truck

speed of light

Result

For speeds far less than c, relativity is barely noticeable

b) Length Contraction (things shrink)

a) Time Dilation (time slows down)

For greater speeds, observers in different reference frames experience:

Time Dilation

To an observer on the ground, what path

does the light follow?

Now imagine putting it on a spaceship.

Imagine a “light clock”

tt

1 vc

0

2

2

Time Dilation Equation

t0 = proper time (measured in the same reference frame as the events are occurring)

t = time measured by an observer in a different reference frame

v = relative speed between the two reference frames

c = 3.00 x 108 m/s

So what does this all mean ???

tt

1 vc

0

2

2

<1

<1

t > t0

Web Link: Time DilationProof:

2) GPS and airplane navigation must use it in their calculations!

1) Atomic clocks on jets slow by precisely this amount

3) Muons arrive at earth’s surface Web Link: Muon Time Dilation

Time slows down in a reference frame that is moving relative to the observer !

Ex:

An observer on the ground is monitoring an astronaut in a

spacecraft that is traveling at a speed of 5 x 107 m/s .

On average, a human heart beats 70 times per minute. Calculate the time between heartbeats and the number of heartbeats per day for

a) the person on earth (this part is easy)

b) the space traveler, as monitored from earth

So the guy on the ground sees the guy

on the spaceship aging more slowly.

What does the guy on the spaceship see when he looks at the guy on the ground ??

The Twin Paradox

One twin travels at a speed of .80c to a galaxy 8 light years away and and then travels back to earth at the same speed.

Upon his return he will be 8 years younger than his twin!

How is this different from the previous example ??

Understanding Time Dilation

x

y

Constant speed in x-direction

More y-motion, less x-motion

time

space

Sitting still (not moving through space)

More motion through space, less motion through time

Just think of time as the 4th dimension

Length Contraction

L0

Observer (t)

(t0)v

v = relative speed

L0 = proper length (measured by observer at rest with respect to object/distance)

L = length measured from a different reference frame

c = 3.00 x 108 m/s

L L 1 vc0

2

2 Length

Contraction Equation

<1

Web Link: Length Contraction

*Only in the direction of motion:

Distances/lengths appear shorter when moving relative to the observer.

v

Ex: Passing spaceships

spaceship 1 (2.0 x 108 m/s)

spaceship 2 (at rest)

Both have a proper length of 8.5 m.

How long does spaceship 1 look to spaceship 2 ?

How long does spaceship 2 look to spaceship 1 ?

Recall: momentum = p = mv

m1v1 m2

v2

m1v1 + m2v2 = constant

Conservation of Momentum:

When things are moving close to the speed of light, this equation is way off !

We need to consider…

Relativistic Momentum

pm v

1 vc

2

2

<1

>mv

What happens if we use this equation when v is very small ?

Are there any situations in which things move so fast that we have to use this equation?

If we calculate momentum this way for high speeds, conservation of

momentum is obeyed.

Stanford Linear Particle Accelerator

Electrons accelerate to 99.99999997% speed of light !

Momentum is 40,000 times greater than mv !

Em c

1 vc

2

2

2

Total Energy of an Object =

E = mc2 Mass-Energy Equivalence

MassEnergy conserved together

If v=0 : E = mc20

= rest energy

This much energy

is equivalent

to

This much mass

E0 = mc2

A huge amount of

energy

A small mass

The rest energy of a 46 gram golf ball could be used to operate a 75-Watt

light bulb for 1.7 million years!

Our country uses about 3.3 trillion kWhrs of energy per year. Find the amount of mass that is

equivalent to this much energy.

Ex:

E0 = mc2

If energy changes

Mass must change also

When a 1 kg ball falls 200 m and lands on the ground, by how much does its mass change?

Why don’t we notice this ?

More examples of Mass-Energy Equivalence…

Ex: Matter meets antimatter

e-

electron

e+

positron

+ =

gamma rays

2 (9.11x10-31 kg) mass = 0

pure energy

People used to wonder if the moon was made of

antimatter

Ex: Nuclear Power (Fission)

Big nucleus 2 smaller nuclei(less total mass, less energy)

Web Link: Fission

Ex: The Sun (Fusion)

Two small nuclei

(less total mass, less energy)

Larger nucleus

Web Link: Fusion

The sun loses over 4 billion kg per second due to fusion

(Don’t worry, it will last for another 5 billion years or so)

Recall: E0 = mc2 = rest energy

If an object is moving, its total energy is the sum of its rest energy and its kinetic energy:

E = E0 + KE

We can solve for KE… K E m c

1

1 vc

12

2

2

Relativistic Kinetic Energy

What happens to this equation if an object is traveling at the speed of light?

Objects with mass cannot reach the speed of light

Recall that all these effects of Special Relativity would only become noticeable to us as speeds

approach the speed of light.

Let’s try to get an idea of how fast light really is…

Traveling at the speed of light, just how far around the earth could you

go in 1 second?

Particles experience:

Collisions

Waves experience:

Interference

When they are headed for the same place at the same time…

Electrons are…

Particles:-

--

and Waves:Interference

Web Links:Electron Interference

Double Slit Experiment

collisions

Light is…

a Wave:

and a Particle:

light

metal-

-Photoelectric

Effect

Wave-Particle Duality

Light (any electromagnetic wave) is composed of …

Photons – massless energy particles

E = h f

E = Energy of 1 photon

h = Planck’s constant = 6.626 x 10-34 Js

f = frequency of light wave

Ex:

How many photons are emitted in 1 hour by a 25 Watt red light bulb ? ( For red, use =750 nm)

Ex:

Which type of electromagnetic wave is represented by photons with the following energies ?

E = 3.3 x 10-16 J

a)

E = 1.3 x 10-20 J

b)

The Photoelectric Effect

W0 = Work Function = minimum work

required to eject an electron from the metal

Photon E=hf -

Electron with maximum KE

Web Link: Photoelectric Effect

Conservation of Energy: hf = W0 + KEmax

More light does not result in electrons with more KE

Energy is being absorbed in packets (like particles)

No electrons are ejected if the frequency is too low

The Photoelectric Effect in the garage…

More Photoelectric Effect Applications

Photographer’s light meter

Digital Camera

Web Link: Digital Camera

Automatic Doors

Web Link: Solar Energy

Ex:

Sodium (W0=2.28 eV)

White Light (all colors) = 380-750 nm

-

-

Find the maximum kinetic energy of the ejected electrons (in electron-Volts).

(Energy=hf)

(Energy=hf’)

The Compton Effect

Web Link: Compton Effect

Does the photon have more or

less energy after the collision?

The electron now has some Kinetic Energy

Photon Mom entum ph

e

’

e

Conservation of Energy & Conservation of Momentum…

h

m c1 cos m = electron mass

h = Planck’s constant

c = speed of light

hm c

= Compton wavelength = 2.43 x 10-12 m

What is the change in wavelength if =0°? =180°?

Now take a few minutes to discuss these with your group:

Conceptual Example 4 in the textbook (p.905)

Solar Sail

Check Your Understanding #10

(p.906)

Radiometer

When they finally tried it out with electrons, the interference pattern corresponded perfectly

to this wavelength!

OK, so we’ve accepted the fact that waves act like particles

(have momentum, collisions, etc.)p

h

In 1923 Prince Louis de Broglie suggested for the first time that maybe particles act like waves:

hp

De Broglie Wavelength

Ex:

Find the de Broglie wavelength of a car with a mass of 1000 kg traveling at a

speed of 30 m/s.

So what does this wavelength really mean for particles??

It’s a Probability Wave:

100 electrons

3000 electrons70000 electrons

Does the universe exist if we’re not looking???

Web Link:

The Heisenberg Uncertainty Principle

“The more precisely the position is determined, the less precisely

the momentum is known” - Heisenberg, Uncertainty paper, 1927

If x = uncertainty in position,

and p = uncertainty in momentum,

then

x ph

4

Ex:

Within an atom, the uncertainty in an electron’s position is 10-10 m (the size of the atom).

Find the uncertainty in the electron’s speed.

Ex:

The marble (m=25 g) is somewhere within the box. Find the uncertainty in the marble’s speed.

10 cm

Heisenberg is out for a drive when he’s stopped by a traffic cop. The cop says “Do you

know how fast you were going?”

Heisenberg says “No, but I know where I am.”

There is another form of Heisenberg’s Uncertainty Principle that involves Energy and Time:

If E = uncertainty in a particle’s energy,

and t = the time it has that energy,

then

E th

4

Web Links: Scanning Tunneling Microscope Animated STM

STM images

This leads to “Quantum Tunneling”

The best part about knowing all this physics, is that now you

will get the jokes……

A Party of Famous Physicists

Let’s see how many of the following physicists you can guess…

Everyone was attracted to his magnetic personality.

He was under too much pressure to enjoy himself.

He may or may not have been there.

?

??

He went back to the buffet table several times a minute.

He turned out to be a powerful speaker.

He got a real charge out of the whole thing.

He thought it was a relatively good time.