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PHYS 202: University Physics II
Course Description
This course aims to explain physics in a readable and interesting manner that is accessible and clear, and to teach students by anticipating their needs and difficulties without oversimplifying. Physics is a description of reality, and thus each topic begins with concrete observations and experiences that students can directly relate to. We then move on to the generalizations and more formal treatment of the topic. Not only does this make the material more interesting and easier to understand, but it is closer to the way physics is actually practiced.
Course Objectives:
1. To describe, in words, the ways in which various concepts in electromagnetism come into play in particular situations;
2. To represent these electromagnetic phenomena and fields mathematically in those situations;
3. And to predict outcomes in other similar situations.
Week 1/Week 1/First Exam.pdf
MID TERM Exam 1 Name
1. (8) A tiny plastic sphere is initially neutral. Then after being rubbed by a piece of fur, it acquires a net charge of +2.4 nC. How many electrons were transferred [ to / from ] (← select one) the sphere?
2. (6) A balloon acquires a negative charge when rubbed on a sweater.
a) (3) As a result, the charge acquired by the sweater is a. negative b. zero c. positive.
b) (3) T F Electrons were lost by the sweater in the balloon charging process.
3. (20) Two charges, Q1 = +4.2 µC and Q2 = −8.8 µC are separated by 12.0 cm on the x-axis as shown. The charges produce an electric field in the surrounding region. Consider only the electric field along the x-axis.
a) (3) T F At any point between the charges, their net electric field points to the left.
b) (3) T F To the left of Q1, there is a point at finite x where the electric field is zero.
c) (8) Determine the magnitude and direction of the net electric field 12.0 cm to the left of Q1.
d) (6) If a third charge q = 2.0 µC is now placed 12.0 cm to the left of Q1, what magnitude electric force will it experience?
1
4. (12) Suppose you have a gram of water (H2O, with molar masses H=1.00 g/mole, O=16.0 g/mole).
a) (6) How many water molecules are present in the sample?
b) (6) If one electron is removed from each water molecule, what is the net electric charge of the sample?
Questions about charges.
5. (2) T F In a conductor like copper metal, all of its electrons are free to move.
6. (2) T F The net charge of a piece of metal is the same as its free charge.
7. (2) T F A Van de Graaff generator cannot attract neutral objects.
8. (2) T F Net charge of a conductor distributes itself throughout the volume of the object.
Questions about electric fields.
9. (2) T F Electric field lines point towards negative charges and away from positive charges.
10. (2) T F The electric field inside a conductor carrying a current is zero.
11. (2) T F Electric field lines close together indicate weak electric field strength.
12. (2) T F A region with parallel electric field lines has a constant electric potential.
13. (12) The sphere on a Van de Graaff generator has a radius of 22 cm. The air next to the sphere becomes conducting if the electric field strength reaches 3.0 MV/m. The generator charges the sphere with electrons.
a) (6) What is the charge of maximum magnitude that the sphere can hold without discharging?
b) (6) For that maximum charge on the sphere, what is its electrostatic potential, including the sign? The potential is assumed to be zero very far from the sphere.
2
Questions about electric potential.
14. (2) T F The electric field strength is a constant on any equipotential surface.
15. (2) T F All points of a conductor with static charges are at the same electric potential.
16. (2) T F Electric field lines point towards regions of higher electric potential.
17. (2) T F An electron-volt is the same as 1.602 × 10−19 volts.
18. (20) Two parallel metal plates separated by 5.0 cm are given equal and opposite charges, producing a nearly uniform electric field of strength E = 250 N/C between them.
a) (2) The electric field caused by the charged plates points
a. parallel to the plates. b. towards the positive plate. c. towards the negative plate.
b) (6) Calculate the electric potential difference (in volts) between the plates, ∆V = VB − VA, where A is the negative plate and B is the positive plate.
c) (6) What change in kinetic energy does an electron moving from plate A to plate B experience, in joules?
d) (6) What is the answer to part c), in electron-volts?
19. (12) A capacitor of unknown value is initially uncharged. When now connected to a 48.0-volt battery, it is noticed that 12.0 µC of charge flows from the positive terminal of the battery during a brief interval of time.
a) (6) What is the capacitance of the capacitor?
3
b) (6) Once fully charged, what electrical potential energy is stored in the capacitor?
20. (18) An ideal 12.4-volt car battery sends a current of 28.2 amperes through the starter motor of a car during a time interval of 4.80 seconds.
a) (6) During the 4.80 seconds, how much charge flowed out of the positive terminal of the battery?
b) (6) What electrical power (in watts) is the starter motor using?
c) (6) What is the resistance (in ohms) of the starter motor?
21. (12) Suppose you have a 24.0-watt lightbulb that operates on 120.0 V DC.
a) (6) What current does the lightbulb draw when turned on?
b) (6) What is the resistance of the lightbulb, in ohms?
4 .
Prefixes a=10−18, f=10−15, p=10−12, n=10−9, µ = 10−6, m=10−3, c=10−2, k=103, M=106, G=109, T=1012, P=1015
Physical Constants
k = 1/4π�0 = 8.988 GN·m2/C2 (Coulomb’s Law) �0 = 1/4πk = 8.854 pF/m (permittivity of space) e = 1.602 × 10−19 C (proton charge) me = 9.11 × 10−31 kg (electron mass) mp = 1.67 × 10−27 kg (proton mass)
Units and Conversions
NA = 6.02 × 1023/mole (Avogadro’s #) 1 u = 1 g/NA = 1.6605 × 10−27 kg (mass unit) 1.0 eV = 1.602 × 10−19 J (electron-volt) 1 V = 1 J/C = 1 volt = 1 joule/coulomb 1 F = 1 C/V = 1 farad = 1 C2/J 1 A = 1 C/s = 1 ampere = 1 coulomb/second 1 Ω = 1 V/A = 1 ohm = 1 J·s/C2
Vectors
Written ~V or V, described by magnitude=V , direction=θ or by components (Vx, Vy). Vx = V cos θ, Vy = V sin θ,
V = √
V 2x + V 2y , tan θ = Vy Vx
. θ is the angle from ~V to +x-axis.
Addition: A + B, head to tail. Subtraction: A − B is A + (−B), −B is B reversed.
Trig summary
sin θ = (opp) (hyp)
, cos θ = (adj) (hyp)
, tan θ = (opp) (adj)
, (opp)2 + (adj)2 = (hyp)2.
sin θ = sin(180◦ − θ), cos θ = cos(−θ), tan θ = tan(180◦ + θ), sin2 θ + cos2 θ = 1.
Charges: Q = ±N e, ∆Q1 + ∆Q2 = 0, e = 1.602 × 10−19 C.
Electric Force: F = k Q1Q2
r2 , k = 8.988 × 109 N·m2/C2, F = Q1Q2
4π�0r2 , �0 = 14πk = 8.854 pF/m.
~F = ~F1 + ~F2 + ~F3 + ... superposition of many forces. Fx = F1x + F2x + F3x + ... superposition of x-components of many forces. Fy = F1y + F2y + F3y + ... superposition of y-components of many forces.
Electric Field: ~E =
~F q , q= test charge. Or: ~F = q ~E.
|~E| = E = k Q r2
= Q 4π�0r2
, due to point charge. Negative Q makes inward ~E, positive Q makes outward ~E. ~E = ~E1 + ~E2 + ~E3 + ... superposition of many electric fields. Ex = E1x + E2x + E3x + ... superposition of x-components of many electric fields. Ey = E1y + E2y + E3y + ... superposition of y-components of many electric fields. E = k Q
r2 = electric field around a point charge or outside a spherical charge distribution.
Potential Energy and Work: Wba = FE d cos θ = work done by electric force FE on test charge, in displacement d from a to b. Wba = −q∆V = −q(Vb − Va) = work done by electric force on a test charge, moved from a to b. ∆PE = q∆V = q(Vb − Va) = change in electric potential energy of the system. Also: ∆PE = −Wba. ∆KE + ∆P E = 0, or, ∆KE = −∆P E = −q∆V , principle of conservation of mechanical energy.
Potential: ∆V = ∆PE
q = definition of change in electric potential.
∆V = Ed = potential change in a uniform electric field. V = k Q
r = potential produced by a point charge or outside a spherical charge distribution.
PE = qV = potential energy for a test charge at a point in a field. PE = k Q1Q2
r12 = potential energy of a pair of charges.
Capacitance: Q = CV , C = K�0 Ad = capacitor equations.
U = 1 2 QV = 1
2 CV 2 = 1
2 Q2
C = stored energy.
E = Q/A �0
= electric field strength very near a charged conductor.
Electric current: I = ∆Q
∆t , or ∆Q = I∆t, definition of current.
V = IR, or I = V /R, Ohm’s law. R = ρ L
A = calculation of resistance.
ρT = ρ0[1 + α(T − T0)] = temperature-dependent resistivity. Electric power:
P = IV , P = I2R, P = V 2/R, P = instantaneous energy/time. Alternating current:
V = V0 sin 2πf t = time-dependent AC voltage. I = I0 sin 2πf t = time-dependent AC current.
Vrms = √
V 2 = V0/ √
2 = root-mean-square voltage. Irms = √
I2 = I0/ √
2 = root-mean-square current. AC power in resistors:
P = 1 2 I20 R =
1 2 V 20 /R =
1 2 I0V0 = average power. P = I2rmsR = V
2 rms/R = IrmsVrms = average power.
Week 1/Week 1/1.pdf
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Physics Notes Class 11 CHAPTER 12 THERMODYNAMICS
The branch dealing with measurement of temperature is called thremometry and the devices
used to measure temperature are called thermometers.
Heat
Heat is a form of energy called thermal energy which flows from a higher temperature body to
a lower temperature body when they are placed in contact.
Heat or thermal energy of a body is the sum of kinetic energies of all its constituent particles,
on account of translational, vibrational and rotational motion.
The SI unit of heat energy is joule (J).
The practical unit of heat energy is calorie.
1 cal = 4.18 J
1 calorie is the quantity of heat required to raise the temperature of 1 g of water by 1°C.
Mechanical energy or work (W) can be converted into heat (Q) by 1 W = JQ
where J = Joule’s mechanical equivalent of heat.
J is a conversion factor (not a physical quantity) and its value is 4.186 J/cal.
Temperature
Temperature of a body is the degree of hotness or coldness of the body. A device which is used
to measure the temperature, is called a thermometer.
Highest possible temperature achieved in laboratory is about 108 while lowest possible
temperature attained is 10-8 K.
Branch of Physics dealing with production and measurement temperature close to 0 K is known
as cryagenics, while that deaf with the measurement of very high temperature is called pyromet
Temperature of the core of the sun is 107 K while that of its surface 6000 K.
NTP or STP implies 273.15 K (0°C = 32°F).
Different Scale of Temperature
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1. Celsius Scale In this scale of temperature, the melting point ice is taken as 0°C and the boiling point of water as 100°C and space between these two points is divided into 100
equal parts
2. Fahrenheit Scale In this scale of temperature, the melt point of ice is taken as 32°F and the boiling point of water as 211 and the space between these two points is divided into
180 equal parts.
3. Kelvin Scale In this scale of temperature, the melting pouxl ice is taken as 273 K and the boiling point of water as 373 K the space between these two points is divided into
100 equal pss
Relation between Different Scales of Temperatures
Thermometric Property
The property of an object which changes with temperature, is call thermometric property.
Different thermometric properties thermometers have been given below
(i) Pressure of a Gas at Constant Volume
where p, p100. and pt, are pressure of a gas at constant volume 0°C, 100°C and t°C.
A constant volume gas thermometer can measure tempera from – 200°C to 500°C.
(ii) Electrical Resistance of Metals
Rt = R0(1 + αt + βt 2 )
where α and β are constants for a metal.
As β is too small therefore we can take
Rt = R0(1 + αt)
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where, α = temperature coefficient of resistance and
R0 and Rt, are electrical resistances at 0°C and t°C.
where R1 and R2 are electrical resistances at temperatures t1 and t2.
where R100 is the resistance at 100°C.
Platinum resistance thermometer can measure temperature from —200°C to 1200°C.
(iii) Length of Mercury Column in a Capillary Tube
lt = l0(1 + αt)
where α = coefficient of linear expansion and l0, lt are lengths of mercury column at 0°C and
t°C.
Thermo Electro Motive Force
When two junctions of a thermocouple are kept at different temperatures, then a thermo-emf is
produced between the junctions, which changes with temperature difference between the
junctions. Thermo-emf
E = at + bt 2
where a and b are constants for the pair of metals.
Unknown temperature of hot junction when cold junction is at 0°C.
Where E100 is the thermo-emf when hot junction is at 100°C.
A thermo-couple thermometer can measure temperature from —200°C to 1600°C.
Thermal Equilibrium
When there is no transfer of heat between two bodies in contact, the the bodies are called in
thermal equilibrium.
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Zeroth Law of Thermodynamics
If two bodies A and B are separately in thermal equilibrium with thirtli body C, then bodies A
and B will be in thermal equilibrium with each other.
Triple Point of Water
The values of pressure and temperature at which water coexists inequilibrium in all three states
of matter, i.e., ice, water and vapour
called triple point of water.
Triple point of water is 273 K temperature and 0.46 cm of mere pressure.
Specific Heat
The amount of heat required to raise the temperature of unit mass the substance through 1°C is
called its specific heat.
It is denoted by c or s.
Its SI unit is joule/kilogram-°C'(J/kg-°C). Its dimensions is [L 2 T
-2 θ
-1 ].
The specific heat of water is 4200 J kg -1
°C -1
or 1 cal g -1
C -1
, which high compared with most
other substances.
Gases have two types of specific heat
1. The specific heat capacity at constant volume (Cv). 2. The specific heat capacity at constant pressure (Cr).
Specific heat at constant pressure (Cp) is greater than specific heat constant volume (CV), i.e.,
Cp > CV .
For molar specific heats Cp – CV = R
where R = gas constant and this relation is called Mayer’s formula.
The ratio of two principal sepecific heats of a gas is represented by γ.
The value of y depends on atomicity of the gas.
Amount of heat energy required to change the temperature of any substance is given by
Q = mcΔt
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where, m = mass of the substance,
c = specific heat of the substance and
Δt = change in temperature.
Thermal (Heat) Capacity
Heat capacity of any body is equal to the amount of heat energy required to increase its
temperature through 1°C.
Heat capacity = me
where c = specific heat of the substance of the body and m = mass of the body.
Its SI unit is joule/kelvin (J/K).
Water Equivalent
It is the quantity of water whose thermal capacity is same as the heat capacity of the body. It is
denoted by W.
W = ms = heat capacity of the body.
Latent Heat
The heat energy absorbed or released at constant temperature per unit mass for change of state
is called latent heat.
Heat energy absorbed or released during change of state is given by
Q = mL
where m = mass of the substance and L = latent heat.
Its unit is cal/g or J/kg and its dimension is [L 2 T
-2 ].
For water at its normal boiling point or condensation temperature (100°C), the latent heat of
vaporisation is
L = 540 cal/g
= 40.8 kJ/ mol
= 2260 kJ/kg
For water at its normal freezing temperature or melting point (0°C), the latent heat of fusion is
L = 80 cal/ g = 60 kJ/mol
= 336 kJ/kg
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It is more painful to get burnt by steam rather than by boiling was 100°C gets converted to
water at 100°C, then it gives out 536 heat. So, it is clear that steam at 100°C has more heat than
wat 100°C (i.e., boiling of water).
After snow falls, the temperature of the atmosphere becomes very This is because the snow
absorbs the heat from the atmosphere to down. So, in the mountains, when snow falls, one does
not feel too but when ice melts, he feels too cold.
There is more shivering effect of ice cream on teeth as compare that of water (obtained from
ice). This is because when ice cream down, it absorbs large amount of heat from teeth.
Melting
Conversion of solid into liquid state at constant temperature is melting.
Evaporation
Conversion of liquid into vapour at all temperatures (even below boiling point) is called
evaporation.
Boiling
When a liquid is heated gradually, at a particular temperature saturated vapour pressure of the
liquid becomes equal to atmospheric pressure, now bubbles of vapour rise to the surface d
liquid. This process is called boiling of the liquid.
The temperature at which a liquid boils, is called boiling point The boiling point of water
increases with increase in pre sure decreases with decrease in pressure.
Sublimation
The conversion of a solid into vapour state is called sublimation.
Hoar Frost
The conversion of vapours into solid state is called hoar fr..
Calorimetry
This is the branch of heat transfer that deals with the measorette heat. The heat is usually
measured in calories or kilo calories.
Principle of Calorimetry
When a hot body is mixed with a cold body, then heat lost by ha is equal to the heat gained by
cold body.
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Heat lost = Heat gain
Thermal Expansion
Increase in size on heating is called thermal expansion. There are three types of thermal
expansion.
1. Expansion of solids 2. Expansion of liquids 3. Expansion of gases
Expansion of Solids
Three types of expansion -takes place in solid.
Linear Expansion Expansion in length on heating is called linear expansion.
Increase in length
l2 = l1(1 + α Δt)
where, ll and l2 are initial and final lengths,Δt = change in temperature and α = coefficient of
linear expansion.
Coefficient of linear expansion
α = (Δl/l * Δt)
where 1= real length and Δl = change in length and
Δt= change in temperature.
Superficial Expansion Expansion in area on heating is called superficial expansion.
Increase in area A2 = A1(1 + β Δt)
where, A1 and A2 are initial and final areas and β is a coefficient of superficial expansion.
Coefficient of superficial expansion
β = (ΔA/A * Δt)
where. A = area, AA = change in area and At = change in temperature.
Cubical Expansion Expansion in volume on heating is called cubical expansion.
Increase in volume V2 = V1(1 + γΔt)
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where V1 and V2 are initial and final volumes and γ is a coefficient of cubical expansion.
Coefficient of cubical expansion
where V = real volume, AV =change in volume and Δt = change in temperature.
Relation between coefficients of linear, superficial and cubical expansions
β = 2α and γ = 3α
Or α:β:γ = 1:2:3
2. Expansion of Liquids
In liquids only expansion in volume takes place on heating.
(i) Apparent Expansion of Liquids When expansion of th container containing liquid, on
heating is not taken into accoun then observed expansion is called apparent expansion of
liquids.
Coefficient of apparent expansion of a liquid
(ii) Real Expansion of Liquids When expansion of the container, containing liquid, on heating
is also taken into account, then observed expansion is called real expansion of liquids.
Coefficient of real expansion of a liquid
Both, yr, and ya are measured in °C -1
.
We can show that yr = ya + yg
where, yr, and ya are coefficient of real and apparent expansion of liquids and yg is coefficient
of cubical expansion of the container.
Anamalous Expansion of Water
When temperature of water is increased from 0°C, then its vol decreases upto 4°C, becomes
minimum at 4°C and then increases. behaviour of water around 4°C is called, anamalous
expansion water.
3. Expansion of Gases
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There are two types of coefficient of expansion in gases
(i) Volume Coefficient (γv) At constant pressure, the change in volume per unit
volume per degree celsius is called volume coefficient.
where V0, V1, and V2 are volumes of the gas at 0°C, t1°C and t2°C.
(ii) Pressure Coefficient (γp) At constant volume, the change in pressure per unit pressure per
degree celsius is called pressure coefficient.
where p0, p1 and p2 are pressure of the gas at 0°C, t1° C and t2° C.
Practical Applications of Expansion
1. When rails are laid down on the ground, space is left between the end of two rails. 2. The transmission cables are not tightly fixed to the poles. 3. The iron rim to be put on a cart wheel is always of slightly smaller diameter than that of
wheel.
4. A glass stopper jammed in the neck of a glass bottle can be taken out by warming the neck of the bottles.
Important Points
Due to increment in its time period a pendulum clock becomes slow in summer and will
lose time.
Loss of time in a time period ΔT =(1/2)α ΔθT
∴ Loss of time in any given time interval t can be given by ΔT =(1/2)α Δθt
At some higher temperature a scale will expand and scale reading will be lesser than true
values, so that
true value = scale reading (1 + α Δt)
Here, Δt is the temperature difference.
However, at lower temperature scale reading will be more or true value will be less.
Week 1/Week 1/2.pdf
1
Electric Charges, Forces and Fields
Chapter 17
2
Forces of Nature
Electric Charge
Coulomb’s Law
Electric Field
Electric Field Lines
Flux of an Electric Field
Forces of nature or
A short journey … back to Physics 111
Part 1
4
Physics 111: Analysis of motion - 3 key ideas
Newton’s laws of motion
Conservation of Energy
Conservation of Momentum
5
Newton’s laws of motion
Newton’s First Law: If no force acts on a body, then the body’s velocity cannot change
Newton’s Second Law: amF =
Newton’s laws of motion allow us to analyze many kinds of motion.
6
Newton’s laws of motion (applications)
amF =
atvv
at tvxx
+=
++=
0
2
00 2
Special case: motion with constant acceleration (1D, 2D or 3D motion)
Observables: time force position velocity acceleration
Examples of problems: projectile motion, …
2
7
Conservation of energy
ffii UKUK +=+
In an isolated system where only conservative forces cause energy changes, the kinetic energy and potential energy can change, but their sum cannot change
The total energy of an isolated system cannot change
8
Conservation of momentum
constvmvmvmP nn =+++= rrrr
...2211
Conservation of linear momentum If no net external force acts on a system of particles, the total linear momentum of the system cannot change
Conservation of angular momentum If the net external torque acting on a system is zero, the angular momentum of the system remains constant, no matter what changes take place within the system
fi LL rr
=
9
What forces do we know from our experience and Physics 111?
Gravitational Force Frictional Force Spring Force (Hook’s Law) Normal Force Tension force in a string Aerodynamic Drag Force ……
10
There are ONLY four fundamental forces of nature
11
FOUR or ONE?
Many scientists think that all four of the fundamental forces are, the manifestations of a single force which has yet to be discovered.
Just as electricity, magnetism, and the weak force were unified into the electroweak interaction, they work to unify all of the fundamental forces.
12
Gravitational and electro-magnetic forces: this what we experience!!!
Frictional force, spring force, normal force, tension force in a string, aerodynamic force … are results of electromagnetic force
3
Electric Charge
Part 2
14
Electric charge
Electric Charge is an intrinsic characteristic of the fundamental particles making up objects around us (including us).
The ordinary matter consists of three (only!) particles:
0.001.60×10-19 C-1.60×10-19 Ccharge
1.67×10-27 kg1.67×10-27 kg9.11×10-31 kgmass
neutron (n)proton (p)electron (e)
The SI unit of electric charge is the Coulomb
15
Important characteristic of electric charge
An electric charge has a magnitude and sign. It is either positive or negative. Electron has negative electric charge Proton has positive electric charge
If the charges have the same sign, the forces between them are repulsive
Charges of opposite sign experience attractive forces 16
Atoms and molecules are made up from electrons, protons and neutrons!
A classical (solar system) model of an atom (Lithium)
A quantum model of an atom (Lithium)
Atoms are combinations of equal amounts of electrons and protons.
17
Sizes and masses Atoms are combinations of equal amounts of electrons and protons. The neutrons provide the glue to stick together the protons in the nucleus. The proton and the neutron are about 2000 times heavier than the electron, so the vast majority of an atom’s mass resides in the nucleus. Atoms are mostly … empty. We live in almost empty space
Example: tennis ball and a grain of sand 18
Net electric charge for a system of n particles
The total (net) electric charge of an isolated system is conserved. The only way to change it is to add or remove charged particles.
nnet qqqqq K+++= 321
the net electric charge of atoms and molecules is zero (equal amounts of electrons and protons) removing an electron from a neutral atom creates a positive ion negative ions?
The total electric charge of the universe is constant.
4
19
Example:
20
21
To make an uncharged object have a negative charge we must: A) add some atoms B) add some protons C) add some electrons D) add some neutrons E) write down a negative sign
?
22
Macro objects (many atoms or molecules)
Materials – two extreme models Insulators – a material in which charges do not move freely though the interior of the sample. Examples: Glass, wood, rubber, plastics, stone, brick, etc Conductors – material where free charges can move through the material. Examples: Ionized gases (plasmas), metals, ionic solutions if salts in water Semi-conductors – a material intermediate between the two extreme models – GaAs, Ge, Si, are the classic examples.
23
Macro objects can be charged by charge transfer or charge separation
Charge transfer happens when electric charges (usually electrons) transfer from one object to another Charge separation occurs when two material are rubbed together or when objects collide
24
Charge is quantized
Experiments show that any positive or negative charge q that can be detected can be written as
where e is the elementary charge.
Ce nenq
191060.1 ,3,2,1,
−×=
±±±=⋅= K
5
25
from a simple to complex
Universe
human beings
cells
condense matter, gases
molecules
atoms
electrons, protons, neutrons
fundamental particles: electrons, quarks, …
Note: ALL electrons are identical, as well as protons, neutrons …
A force between charges
Part 3
27
Coulomb’s Law
The electrostatic force between two charges q1 and q2 separated by a distance r has the magnitude
2 21 ||
r qq
kF =
k is the electromagnetic constant ε0 is the permittivity constant
Where is the 3rd Newton’s law?
/CN·m 108.99 4
1 k 229
0
×== πε
28
The diagram shows two pairs of heavily charged plastic cubes. Cubes 1 and 2 attract each other and so do cubes 1 and 3.
Which of the following illustrates the forces of 2 on 3 and 3 on 2?
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29
Comparing the gravitational and electrostatic forces
Let’s calculate the ratio of the electrical to the gravitational force inside a hydrogen atoms.
2 2
2
,p e e p eg e
e p e
e
g
GM M k q q F F
R r k q q
F r F
= =
=
2 p eGM M
r 9 19 2
11 27 31
39
(9 10 )(1.6 10 ) (6.67 10 )(1.67 10 )(9.11 10 )
2.27 10
e p e
p e
e
g
k q q GM M
F F
−
− − −
=
× × =
× × ×
= × So we can forget gravity as compared to electrostatic forces – at least on the atomic scale 30
A contradiction to a simple observation?
If Fe/FGl =2.27×1039 then, why the gravity force plays any observable role?
The force of gravity play essentially NO role in atomic and molecular systems However macroscopic objects are neutral or almost neutral (the net electric charge is close to zero) Therefore the force of gravity play strong role for macroscopic objects
6
31
An example with two coins?
Let’s find an electrostatic force between two coins separated by a distance of 1 meter
a) force between 2 electrons
b) force between electrons in the two coins
c) the net force between electrons and protons in the two coins
electrons 10N C 101.60e
/CN·m 108.99 k
22 coin
19-
229
≈
×=
×=
2 21
r qq
kF =
2.30*10-28 N
2.30*1016 N
0.0 N
about 25 millions!!! 32
Coulomb’s law and the principle of superposition The principle of superposition: the net effect is the sum of the individual effects For n interacting particles the net force on particle 1 can be written as
nnet FFFFF 1141312,1 r
K rrrr
+++=
being practical – see chapter 3 “Vectors in Physics” (adding vectors using components)
33
Net Force and the superposition principle Charges Q, –Q, and q are placed at the vertices of an equilateral triangle as shown. The total force exerted on the charge q is: A) toward charge Q B) toward charge –Q C) away from charge Q D) at right angles to the line joining Q and –Q E) parallel to the line joining Q and –Q
Always draw a free body diagram!
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34
Net Force Two point charges are arranged as shown, where Q1 = -2C, Q2 = 1C. In which region could a third charge +1 C be placed so that the net electrostatic force on it is zero?
A) I only B) I and II only C) III only D) I and III only E) II only
What if the third charge is q=-1C?
What if the particles have charges Q and -Q?
What if the particles have charges Q and Q?
?
35
Net Force Consider the three electric charges shown in the figure. List the charges in order of the magnitude of the force they experience, starting with the smallest (Note: the distance from A to B is the same as the distance from B to C.)
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36
Net Force 2
Four identical point charges are placed at the corners of a square. A fifth point charge placed at the center of the square experiences zero net force. Is this a stable equilibrium for the fifth charge
good to use PhET computer simulation as an illustration
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7
37
Example: 3 electric charges in a line Given that q = +12 mC and d = 16 cm,
(a) find the direction and magnitude of the net electrostatic force exerted on the point charge q2 in Figure below?
(b) How would your answers to part (a) change if the distance d were tripled?
problem
38
9 2 2
0
1 3.0 2.0 3.0 2.0 9 10
4blue q q q q
F d dπε × ×
= = × ×
9 2 2
0
1 1.0 2.0 1.0 2.0 9 10
4red q q q q
F d dπε × ×
= = × ×
9 resultant 2 2
3.0 2.0 1.0 2.0 9 10 to the right
q q q q F
d d × ×⎡ ⎤
= × × −⎢ ⎥⎣ ⎦
problem
39
problem
40
problem
A tale of two particles An electron and a proton are released from rest in space, far from any other object. The particles move toward each other, due to their mutual attraction. When they meet, is the kinetic energy of the electron greater than, less than, or the same as the kinetic energy of the proton? Explain.
Electric Field
Part 4
42
A couple “simple” questions The Coulomb law
2 21
r qq
kF =
How does q1 “know” of the presence of q2?
Since the charges do not touch, how can q1 exert a force on q2?
Action on a distance!
Other examples?
8
43
Electric Fields or Action on a Distance
We can say that q1 sets up an electric field in the space surrounding it.
1. At any given point P in that space the field has both magnitude and direction.
2. The magnitude depends on the magnitude of q1 and the distance between P and q1.
3. The direction depends on the direction from q1 to P and the electrical sign of q1.
4. Thus when we place q2 at P, q1 interacts with q2 through the electric field at P.
44
The electric field is a vector field
The electric field consists of a distribution of vectors, one for each point in the region around a charged object. A way to define the electric field at some point P
1. Place a positive charge q0, called a test charge, at the point P
2. Measure the electrostatic force that acts on the test charge
3. Define the electric field at the point P due to the charged object as
F
0q F
E =
The SI unit for the electric field is the newton per coulomb (N/C)
45
A particle in an electric field
1. If we know the electric field vector at a given point, the force that a charge q experiences at that point is
2. The direction of the force: positive particles – in the direction of the field negative particles – in the opposite direction of the field
EqF rr
=
E r
+F r−
F r
46
The electric field due to a point electric charge
From Coulomb’s law, the magnitude of the electrostatic force acting on q0 is
The direction of the force is directly away from the point charge if q is positive, and directly toward the point charge is q is negative. Then the magnitude of the electric field from a point charge is
2 0
0 2
0
4 1
r qq
r qq
kF πε
==
2 0
2 4 1
r q
r q
kE πε
==
47
Example
Electric field around a positive electric charge
48
The electric field due to more than one point electric charge
Using the superposition principle we can find the net force
Therefore the net electric field at the position of the test charge is
nnet FFFFF 0030201,0 r
K rrrr
+++=
0
0
0
03
0
02
0
01
0
,0
q F
q F
q F
q F
q F
E nnet r
K
rrrr
+++==
nEEEEE 0030201 K+++=
9
49
Net Field
A proton p and an electron e are on the x axis. Find the directions of the electric field at points 1, 2, and 3 respectively
Go to PhET
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50
Consider two identical negative charges as shown. At which lettered point is the magnitude of the electric field greatest? Least?
−−a d cb
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51
Conceptual question A proton moves in a region of constant electric field.
Does it follow that the proton’s velocity is parallel to the electric field?
Does it follow that the proton’s acceleration is parallel to the electric field?
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52
Conceptual question The force experienced by charge 1 at point A is different in direction and magnitude from the force experienced by charge 2 at point B.
Can we conclude that the electric fields at point A and point B are different?
?
53
Example: a point charge in an electric field
The essential features of an ink-jet printer
amEqF r
==
then … motion with constant acceleration (see physics 111)
54
Tools (equations) to describe motion of electrons
amEqF r
==
Second Newton’s lawclassical mechanics gases, plasma, …
Schrodinger equation Dirac equation
quantum mechanics
atoms molecules
10
Electric Field Lines
Part 5
56
Electric field lines provide a nice way to visualize patterns in electric fields
1. At any point, the direction of a straight field line gives the direction of the electric field at that point
2. Electric fields extend away from positive charge and toward negative charge
3. No field lines cross. 4. The field lines are drawn so that the
number of lines per unit area is proportional to the magnitude of the electric field.
57
Examples
Note that twice as many field lines originate from the +2q charge than the +q or –q charges.
58
Problem
The electric field lines surrounding three charges are shown in the Figure. The center charge is q2 = - 10.0 mC.
(a) What are the signs of q1 and q3?
(b) Find q1.
(c) Find q3.
Flux of an Electric Field
Part 6
60
Flux
Example: a wide air stream of uniform velocity at a small square loop of area A. Let Φ represents the volume flow rate (volume per unit time) at which air flows through the loop. The rate depends on the angle between the velocity and the plane of the loop.
θθ cos)cos( vAAv ==Φ
11
61
Flux of an Electric Field
θ is the angle between the electric field and the line perpendicular to the surface.
SI units: N·m2/C
For a non-uniform fields we have to integrate over a surface
The electric flux through a surface is proportional to the net number of electric field lines passing through that surface.
θcosEA=Φ
62
Gauss’ Law
Gauss’ law relates the net flux Φ of an electric field through a closed surface to the net charge qenc that is enclosed by that surface
encq=Φ0ε
Gauss’ law and Coulomb’s law Demonstration for a point charge
2
2 0
4
4 1
rA
r q
E
π
πε
=
= 0
2 2
0
4 4
1 ε
π πε
q r
r q
EA ===Φ
63
Example In the following figure, the dashed line denotes a Gaussian surface enclosing part of a distribution of four positive charges.
(a) Which charges contribute to the electric field at P?
(b) Is the value of the flux through the surface, calculated using only the electric field due to q1 and q2, greater than, equal to, or less than that obtained using the field due to all four charges?
64
A practical conclusion from the Gauss’s Law – Faraday’s cage
During a thunderstorm – stay in your car!!!
65
A very good collection of interactive simulations to learn physics from the Physics Education Technology project at the University of Colorado http://www.colorado.edu/physics/phet/
Epilogue Interactive Computer Simulation
