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PHYS 1444 – Section 003 Lecture #2AnnouncementsCoulomb’s LawCoulomb’s Law – The FormulaElectric ForceThe Elementary Charge and PermittivityExample 21 – 1Example 21 – 2The Electric FieldSlide 10Example 21 – 5Direction of the Electric FieldField LinesElectric Fields and ConductorsExample 21-13Wednesday, Aug. 31, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu1PHYS 1444 – Section 003Lecture #2Wednesday, Aug. 31, 2005Dr. Jaehoon Yu•Coulomb’s Law•The Electric Field•Field Lines•Electric Fields and Conductors•Motion of a Charged Particle in an Electric Field•Electric Dipoles•CH22: Gauss’ LawWednesday, Aug. 31, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu2Announcements•Next Monday, Sept. 5, is a Labor day. –No class–Homework due has been changed to noon, Tuesday, Sept. 6, to reflect this.•Your five extra credit points for e-mail subscription is till midnight tonight. Please take a full advantage of the opportunity.–Nine of you have subscribed so far. Thank you!!!•All of you have registered in the homework system.–I am TOTALLY impresssed!!! GOOOOOOOD Job!! –Two of the registered, though, forgot to submit the homework. I will extend the free 100% credit on HW#1 till midnight tonight, unless you don’t want me to….Wednesday, Aug. 31, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu3Coulomb’s Law•Charges exert force to each other. What factors affect the magnitude of this force?–Any guesses?•Charles Coulomb figured this out in 1780’s.•Coulomb found that the electrical force is–Proportional to the multiplication of the two charges•If one of the charges doubles the force doubles.•If both the charges double, the force quadruples.–Inversely proportional to the square of the distances between them.–Electric charge is a fundamental property of matter, just like mass.•How would you put the above into a formula?Wednesday, Aug. 31, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu4•The value of the proportionality constant, k, in SI unit is •Thus, 1C is the charge that gives F~9x109N of force when placed 1m apart from each other.1 2Q Q�Coulomb’s Law – The Formula•Is Coulomb force a scalar quantity or a vector quantity? Unit?–A vector quantity. Newtons•Direction of electric (Coulomb) force is always along the line joining the two objects.–If the two charges are the same: forces are directed away from each other.–If the two charges are opposite: forces are directed toward to each other. •Coulomb force is precise to 1 part in 1016.•Unit of charge is called Coulomb, C, in SI.F1Q1 22Q QF kr=2r�2Q�Formula9 2 28.988 10 N mk C= � �Wednesday, Aug. 31, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu5Electric Force•Does the electric force look similar to another force? What is it?–Gravitational Force•What are the sources of the forces?–Electric Force: Charges, fundamental properties of matter–Gravitational Force: Masses, fundamental properties of matter•What else is similar?–Inversely proportional to the square of the distance between the sources of the force  What is this kind law called?•Inverse Square Law•What is the difference?–Gravitational force is always attractive.–Electric force depends on the type of the two charges.1 22Q QF kr=and Gravitational Force1 22M MF Gr=ExtremelySimilarWednesday, Aug. 31, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu6The Elementary Charge and Permittivity•Elementary charge, the smallest charge, is that of an electron: –Since electron is a negatively charged particle, its charge is –e.•Object cannot gain or lose fraction of an electron.–Electric charge is quantized.•It changes always in integer multiples of e.•The proportionality constant k is often written in terms of another constant, 0, the permittivity of free space. They are related and . •Thus the electric force can be written:•Note that this force is for “point” charges at rest.191.602 10e C-= �01 4k pe=12 2 201 4 8.85 10k C N me p-= = � �1 22014Q QFrpe=Wednesday, Aug. 31, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu7Example 21 – 1 •Electric force on electron by proton. Determine the magnitude of the electric force on the electron of a hydrogen atom exerted by the single proton (Q2=+e) that is its nucleus. Assume the electron “orbits” the proton at its average distance of r=0.53x10-10m. 1911.602 10Q e C-=- =- �1 2 1 22 2014Q Q Q QF kr rpe= =Using Coulomb’s lawEach charge is1921.602 10Q e C-=+ = �andSo the magnitude of the force is1 22Q QF kr=( ) ( )( )19 199 2 22101.6 10 1.6 109.0 100.53 10C CN m Cm- --� �= � ��88.2 10 N-= �Which direction?Toward each other…Wednesday, Aug. 31, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu8Example 21 – 2 •Which charge exerts greater force? Two positive point charges, Q1=50C and Q2=1C, are separated by a distance L. Which is larger in magnitude, the force that Q1 exerts on Q2 or the force that Q2 exerts on Q1?1 2122Q QF kL=What is the force that Q1 exerts on Q2?Therefore the magnitudes of the two forces are identical!! Well then what is different? The direction.What is the force that Q2 exerts on Q1?2 1212Q QF kL=What is this law?Which direction? Opposite to each other!Newton’s third law, the law of action and reaction!!Wednesday, Aug. 31, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu9The Electric Field•Both gravitational and electric forces act over a distance without touching objects  What kind of forces are these?–Field forces•Michael Faraday developed an idea of field.–Faraday argued that the electric field extends outward from every charge and permeates through all of space.•Field by a charge or a group of charges can be inspected by placing a small test charge in the vicinity and measuring the force on it.Wednesday, Aug. 31, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu10The Electric Field•The electric field at any point in space is defined as the force exerted on a tiny positive test charge divide by the test charge–Electric force per unit charge•What kind of quantity is the electric field?–Vector quantity. Why?•What is the unit of the electric field?–N/C•The magnitude of the electric field at a distance r from a single point charge Q is FEq=rrFEq=2kQq rq=2kQr=2014Qrpe=Wednesday, Aug. 31, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu11Example 21 – 5 •Electrostatic copier. An electrostatic copier works by selectively arranging


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