PHYS 1444 – Section 004 Lecture #2Coulomb’s Law – The FormulaElectric ForceThe Elementary Charge and PermittivityExample 21 – 1Example 21 – 2Solving ProblemsVector ProblemsThe Electric FieldSlide 10Example 21 – 5Direction of the Electric FieldField LinesElectric Fields and ConductorsExample 21-13Wednesday, Jan. 24, 2007 1 PHYS 1444-004, Spring 2007Dr. Andrew BrandtPHYS 1444 – Section 004Lecture #2•Chapter 21–Coulomb’s Law–The Electric Field & Field Lines–Electric Fields and Conductors–Motion of a Charged Particle in an Electric FieldHomework is due 12 pm, Wednesday, Jan. 31.It’s long so start right away; 25 already registered, gotthe 2 extra points, 1 point still availableWednesday Jan. 24, 2007Dr. Andrew BrandtWednesday, Jan. 24, 2007 2 PHYS 1444-004, Spring 2007Dr. Andrew Brandt•The value of the proportionality constant, k, in SI units is •Thus, if two 1C charges were placed 1m apart the force would be 9x109N.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 two charges have the same sign: forces are directed away from each other.–If two charges are of opposite sign: forces are directed toward each other. •Coulomb’s Law is accurate 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, Jan. 24, 2007 3 PHYS 1444-004, Spring 2007Dr. Andrew BrandtElectric Force•Does the electric force look similar to another force? What is it?–Gravitational Force•What are the sources of the forces?–Electric Force: Charge, fundamental property of matter–Gravitational Force: Mass, fundamental property 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 different?–Gravitational force is always attractive.–Electric force depends on the sign of the two charges.–Magnitude1 22Q QF kr=and Gravitational Force1 22M MF Gr=ExtremelySimilarWednesday, Jan. 24, 2007 4 PHYS 1444-004, Spring 2007Dr. Andrew BrandtThe 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 always occurs 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, Jan. 24, 2007 5 PHYS 1444-004, Spring 2007Dr. Andrew BrandtExample 21 – 1 •Electric force on electron by proton. Determine the magnitude of the electric force on the electron in 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 = 0.53 x10-10 m. (0.5 Angstrom)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?Towards each other…Example on boardWednesday, Jan. 24, 2007 6 PHYS 1444-004, Spring 2007Dr. Andrew BrandtExample 21 – 2 •Which charge exerts greater force? Two positive point charges, Q1=50C and Q2=1C, 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 reactionWednesday, Jan. 24, 2007 7 PHYS 1444-004, Spring 2007Dr. Andrew BrandtSolving Problems •Read and re-read problems carefully•Draw a diagram using arrows to represent vectors•Choose a convenient coordinate system•Note the known and unknown quantities•Write down the relevant relationships•Do an approximate calculation•Solve, substituting numbers only at the end•Keep track of units•Consider if answer is reasonableWednesday, Jan. 24, 2007 8 PHYS 1444-004, Spring 2007Dr. Andrew BrandtVector Problems •Calculate magnitude of vectors (Ex. force using Coulomb’s Law)•Split vectors into x and y components and add these separately, using diagram to help determine sign•Calculate magnitude of resultant |F|=(Fx2+Fy2)•Use = tan-1(Fy/Fx) to get angleExample on boardWednesday, Jan. 24, 2007 9 PHYS 1444-004, Spring 2007Dr. Andrew BrandtThe 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 the idea of a field.–Faraday argued that the electric field extends outward from every charge and permeates through all space.•The field due to 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, Jan. 24, 2007 10 PHYS 1444-004, Spring 2007Dr. Andrew BrandtThe Electric Field•The electric field at any point in space is defined as the force exerted on a tiny positive test charge divided by magnitude of 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•What is the magnitude of the electric field at a distance r from a single point charge Q?FEq=rrFEq=2kQq rq=2kQr=2014Qrpe=Wednesday, Jan. 24, 2007 11 PHYS 1444-004, Spring 2007Dr. Andrew BrandtExample 21 – 5 •Electrostatic copier. An electrostatic copier works by selectively arranging positive charges (in a pattern to be copied) on the surface of a nonconducting drum, then gently sprinkling negatively charged dry toner (ink) onto the drum. The toner particles temporarily stick to the pattern on the drum and are later transferred to paper
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