PHYS 221 General Physics: Electricity, Light and Modern Physics. Lecture 1 Electric Charges & Coulomb s Law. Electric Charge.

Transcription

1 PHYS 1 General Phsics: Electricit, Light and Modern Phsics Lecture 1 Electric Charges & Coulomb s Law Phsics Department Home page: Course Home page: CHIP Home page: Room 144- Undergraduate office Room 11- Help center Room 90- Phsics Librar *Register I-clickers b Wednesda on CHIP reducestatic-cling.html Electric Charge Electric Charge Electric charge is an intrinsic characteristic of the fundamental particles that make up objects. Net charge of a sstem: algebraic sum of all the charges Positive Charge Negative Charge + Electricall neutral: object contains equal amounts of positive and negative charges Net charge: imbalance in charge Law: Conservation of charge The net charge of a closed sstem never changes 1

2 Electric Charge Electric charge is quantized Elementar charge: q = ne, n = ±1, ±,±3,... e = (63) 19 C Coulomb (C): one coulomb is the amount of charge that is transferred through the cross section of a wire in 1 second when there is a current of 1 ampere in the wire. Charge of Particles neutral atom electron orbits e +Ze e e nucleus Particles Smbol Charge Electron Proton Neutron e or e - Nucleus charge= +Ze, atom with Z electrons is neutral. Proton charge: e + = C Electron charge: e - = C p n e - e + 0 Interaction of Charges Charged objects interact b eerting forces on one another. DEMO: 5A-0 Pith Balls Conductors versus Insulators Conductors: material in which electric charges can move around freel. Insulators: material in which electric charges are frozen in place. (metals, tap water, bod) (air, glass, plastic) Semi-conductor: material in which electric charges can move around but not as freel as in conductors. (silicon, germanium) Super-conductor: no resistance to the movement of charge.

3 Interaction of Charges: Insulators Insulators: material in which electric charges are frozen in place. Interaction of Charges: Insulators Force of Repulsion Force of Attraction Charges with the same electrical sign repel each other Charges with opposite electrical signs attract each other. Mobilit of Charge Conductors: material in which electric charges can move around freel. Conductors versus Insulators Demo 5A-04: Charges are more readil transferred b conductors Negativel charged plastic rod will attract either end of the electricall isolated copper rod Reason: charges in copper rod can redistribute themselves. 3

4 Mobilit of Charge Demo: Pie Tins Charging b Induction 1. Bring a charged rod close to conductor. 3. Break connection to ground, keeping the charged rod in place. Ground the conductor. 4. Remove the rod. The sphere is charged. Charge Induction Demo: 5A- Chimes Conducting thread Insulating thread Charged Grounded Coulomb s Law of Electro-static Force q 1 q The electro-static force of attraction/repulsion has a magnitude: where: r k = 1 4" o = Nm / C Coulomb s Law and the permittivit constant is o = 8.55 "1 C / Nm 4

5 Coulomb s Law of Electro-static Force Coulomb s Law of Electro-static Force Force eerted b q 1 on q at a distance r 1 F = k q 1 q r F 1 = kq q 1 r 1, ˆr 1, q 1, q in Coulombs (C) r 1 in meters (m) F 1 in Newtons (N) *Each particle eerts a force of this magnitude on the other particle. *The two forces form an action-reaction pair. F 1 Same sign charges: F 1 is in the direction of r 1,. Opposite sign charges: F 1 is in the direction opposite to r 1,. Coulomb s Law Analogous to Newton s Equation of Gravitation F = k q q 1 F = G m 1m r r * k electro-static constant * Inverse Square Law * Charge *Attractive/repulsive depending on sign of charges *Two kinds of charges *Dominates on small scale Analogous DIFFERS * G gravitational constant * Inverse Square Law * Mass *Alwas attractive *One kind of mass *Dominates on large scales Electro-Static Force versus Newton s Force of Gravitational Attraction DEMO: 4 5

6 Principle of Superposition When several point charges are put together, the total force on an one charge is the vector sum of the each of the separate forces acting on that charge. F = F 1 + F 31 = F 1 Eercise: R=1m F 31 F Q 1 F 1 F = k Q 1 Q r cos 30 0 N " m 9 9 F = F = #3 N C ( #6 C) m ( ) Problem Solving Strategies: Draw a clear FORCE diagram Use consistent units (meter, Coulomb, Newton) Remember that the force is a vector Look for smmetr Q 60 0 Determine force on Q1 Q 1 Q 3 Q 1 =Q =Q 3 =1µC Supplemental Material Three charges on a line F net q = " q q 1 3 = + 3.0" = 3.0" R = " m R C C C net force on q 1 = F 1 + F 31 F 1 = kq q 1 ˆr 1, r 1, F 31 = kq 3q 1 ˆr 1,3 r 1,3 6

7 Keeping subscripts straight and figuring out the directions of ˆr 1, and ˆr 1,3 is tedious. Draw a force diagram. Charges not on a line: need to use components Tr to avoid the temptation to plug in numbers immediatel. Let Q = 1.60 "19 C. Then q 1 = +Q q = +Q q 3 = "Q Also, r 1. = R r 1,3 = 3 4 R q 1 F31 F 1 + = F 1 + F 31 = k " Q R = kq # 7& R $ 9' ( = 14kQ 9R ) 8.96 * 5 N + k " Q = kq # # 3 $ 4 R & R $ 9 ' ( & ' ( Draw a force diagram: F 1 + θ F 41 Find the force on q 1. = F 1 + F 41 ( ) = ( F 1 ) + ( F 41 ) ( ) = 0 + ( F 41 ) ( ) = F 1 + F 41 cos ( ) = 0 + F 41 sin F 1 = θ + F F 41 net = (Fnet ) + (Fnet) tan = ( F 1,net ) (F 1,net ) = F 1 + F 41 = k " Q R + k " Q # 3 $ 4 R & ' ( = kq # & R $ 9 ' ( = kq # 7& R $ 9 ' ( = 14kQ 9R = 14 ) 8.99 ) 9 ) ( 1.60 ) 19 ) ) 9 ).56 ) 38 * 9 ) ( ) ) 4 ) * 7 ) 1.8 ) * 8.96 ) 5 N 7