PHY2049 Physics 2 Lecture Notes Coulomb D. Acosta Page 1 1/5/2008 Coulomb’s Law Disclaimer: These lecture notes are not meant to replace the course textbook. The content may be incomplete. Some topics may be unclear. These notes are only meant to be a study aid and a supplement to your own notes. Please report any inaccuracies to the professor. Electric Charge • It is an intrinsic property of particles (i.e. electrons and protons) • Comes in both positive and negative amounts (assignment of + and – chosen by Ben Franklin) • Usually denote charge by letter “q” (or “Q”), unit of measure is the Coulomb, C, in SI units o Electron: 191.6022 10 Ceqe−=− =− × o Proton: 191.6022 10 Cpqe−== × o In fact, all charge is quantized in integer multiples of “e” (see further below) • Most matter is electrically neutral (balanced: equal amounts + and −) o For example, hydrogen, as with all atoms, is neutral. That is lucky for us, otherwise we would have strong attractions to other pieces of matter. But this observation is not explained by any verifiable theory yet! • Can get a net imbalance of electric charge: o Silk on glass ⇒ excess + charge on glass o Fur on plastic ⇒ excess − charge on plastic • Net charge is always conserved • Like-sign charges repel • Opposite-sign charges attract • Need a force law to describe this! Force Laws Unit of force is Newtons, N, (kg m s-2), in SI units Newton’s Law of Gravity: 1212212ˆgravmmGr=Fr m is mass, measured in kg (SI units). Think of it as the “charge” for gravity. 116.67 10G−=× N m2 kg-2 is Newton’s gravitational constant 12r is the distance between two masses, i.e. 12||r 2 12r 1PHY2049 Physics 2 Lecture Notes Coulomb D. Acosta Page 2 1/5/2008 12ˆr is a unit vector pointing along the direction between mass 1 and mass 2 Note that mass is always defined positive (only one type of gravitational “charge”). Also, the force is always attractive, not repulsive. So the direction of the force is always toward another mass. Coulomb’s Law (Law of Electrostatics, 1785): 1212212ˆcoulqqKr=Fr q is electric charge, measured in C (SI units) 9019104Kπε==× N m2 C-2 is the electrostatic constant [Note: some books use “k”, such as the HRW textbook] 1208.85 10ε−=× C2 N-1 m-2 is the electric permittivity constant Note that electric charge q can be positive or negative. The force is either attractive (opposite charges) or repulsive (like-sign charges). So the direction of the force is either toward another charge (attractive) or oppositely directed from another charge (repulsive). That is, the force is always aligned along 12ˆr . Use this guidance in determining the direction of a force along a particular axis, not the sign of 12qq× directly. Interpretation of force: A force causes an object to accelerate if it is free to move. Newton’s Second Law: m=Fa So for the Coulomb force acting on two charged particles otherwise free to move, the acceleration of one of the particles will be: 11211221112ˆqqKmmr==Far Comparison of Gravitational and Electric Forces: Compare strengths of forces for two objects separated by 1m. Each object has a mass of 1 kg and a charge of 1 C:PHY2049 Physics 2 Lecture Notes Coulomb D. Acosta Page 3 1/5/2008 112920211| | 6.67 10 N111| | 9 10 N 10 | | !1gravcoul gravFGFK F−⋅==×⋅==× >× Compare attractive force between electron and proton in hydrogen: ()()()()()()-31 2711 47221002199840221009.11 10 kg 1.67 10 kg| | 6.67 10 4 10 N0.5 10 m1.6 10 C| | 9 10 N 9 10 N 10 | | !0.5 10 mepgravepcoul gravmmFGaqqFK Fa−−−−−−−××==× =×××==× =× >×× Electric Charge Quantization Experiment done by American physicist Robert Millikan demonstrated that electric charge is quantized. Millikan’s oil drop experiment ⇒ balanced gravitational force, gravF , with electric force, coulF 19 0, 1, 2,... 1.6022 10 Cqne n e−⇒=⋅ =±± = × There exists an elementary unit of charge! No smaller charge observed, although “quarks” (constituents of protons and neutrons) are expected to have fractional electric charges. But nevertheless, quantization is still a unique feature. Electrons: qe=− , protons: qe=+ . We don’t know why balanced! 1 Coulomb of electrons is 18191 C6 10 electrons1.6 10 C−=××! Electric Charge Conservation The net sum of electric charge is always conserved. So when a charged conducting object is brought into contact with another conducting object, the charges in the two objects may redistribute, but the net charge of the combined two-object system will remain the same. Likewise, charge is always conserved in reactions: + + + + + + Fcoul q Fgrav - - - - - - -PHY2049 Physics 2 Lecture Notes Coulomb D. Acosta Page 4 1/5/2008 11238 234 492 90 2pe HeeUThHγγ+−+−+→+→→+ Coulomb’s Law Example (1-dimension) Consider 2 point charges, q1 and q2, separated by a distance x. Let: 123 0 ( is some positive number) (both charges are negative)1 mqqqqqqx=− >=−= Convention: 12Fvdenotes the force acting on particle 1 from the presence of particle 2 Since the force is repulsive (same-sign electric charges), 12 12ˆF=−Fxv (points in negative x direction. Some textbooks denote this by ˆi ). By Newton’s 3rd Law, that for every action (force) there is an equal and opposite reaction, the force on particle 2 from particle 1 is: 21 12 12ˆF=− =FF xvv (points in positive x direction). Again, use this line of reasoning to determine the direction of the force and not the sign in Coulomb’s Law. The magnitude of the force is given by Coulomb’s Law: 21212 122|||||| 3qqFK Kqx== =F Since the force is non-zero and repulsive, the charges will accelerate in the directions specified by the forces. Can we add a third charge to counteract this force and leave all charge stationary? Yes! Place a third positive charge between charges 1 and 2. Note that the superposition principle holds: adding a third charge does not affect the force between charges 1 and 2. Let particle 1 reside at x = 0, particle 2 at x = 1 m, and particle 3 at x = r, where 0 < r < 1. y F12 F21 x q1 q2 x y F12 F13 F23
View Full Document
Unlocking...