Coulomb’s LawElectric ChargeForce LawsNewton’s Law of Gravity:Coulomb’s Law (Law of Electrostatics, 1785):Interpretation of force:Comparison of Gravitational and Electric Forces:Electric Charge QuantizationElectric Charge ConservationCoulomb’s Law Example (1-dimension)Coulomb’s Law Example (2-dimensions)PHY2061 Enriched Physics 2 Lecture Notes CoulombCoulomb’s LawDisclaimer: 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”, unit of measure is the Coulomb, C, in SI unitso Electron:191.6022 10 Ceq e-=- =- �o Proton:191.6022 10 Cpq e-= = �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 glasso 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 LawsUnit of force is Newtons, N, (kg m s-2), in SI unitsNewton’s Law of Gravity:1 212212ˆgravm mGr=F rm 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 constant12r is the distance between two masses, i.e. 12| |r12ˆr is a unit vector pointing along the direction between mass 1 and mass 2D. Acosta Page 1 1/14/2019 2 1PHY2061 Enriched Physics 2 Lecture Notes CoulombNote 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 towardanother mass.Coulomb’s Law (Law of Electrostatics, 1785):1 212212ˆcoulq qKr=F rq is electric charge, measured in C (SI units)9019 104Kpe= = � N m2 C-2 is the electrostatic constant [Note: some books use “k”]1208.85 10e-= � C2 N-1 m-2 is the electric permittivity constantNote 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 1 2q q� directly.Interpretation of force:A force causes an object to accelerate if it is free to move.Newton’s Second Law: m=F aSo for the Coulomb force acting on two charged particles otherwise free to move, the acceleration of one of the particles will be:1 1 21 1221 1 12ˆq qKm m r= =Fa rComparison of Gravitational and Electric Forces:Compare strengths of forces for two objects separated by 1m. Each object has a mass of 1kg and a charge of 1 C:1129 2021 1| | 6.67 10 N11 1| | 9 10 N 10 | | !1gravcoul gravF GF K F-�= = ��= = � > �D. Acosta Page 2 1/14/2019PHY2061 Enriched Physics 2 Lecture Notes CoulombCompare attractive force between electron and proton in hydrogen:( ) ( )( )( )( )( )-31 2711 47221002199 8 40221009.11 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 me pgrave pcoul gravm mF Gaq qF K Fa-- -----� �= = � = ���= = � = � > ��Electric Charge QuantizationExperiment done by American physicist Robert Millikan demonstrated that electric charge is quantized.Millikan’s oil drop experiment -balanced gravitational force, gravF, with electric force, coulF19 0, 1, 2,... 1.6022 10 Cq n e n e-� = � = � � = �There exists an elementary unit of charge!No smaller charge observed, although “quarks” (constituents of protons and neutrons) areexpected to have fractional electric charges. But nevertheless, quantization is still a unique feature. Electrons: q e=-, protons: q e=+. We don’t know why balanced!1 Coulomb of electrons is 18191 C6 10 electrons1.6 10 C-= ��!Electric Charge ConservationThe net sum of electric charge is always conserved. So when a charged conducting objectis brought into contact with another conducting object, the charges in the two objects mayredistribute, but the net charge of the combined two-object system will remain the same. Likewise, charge is always conserved in reactions: 11238 234 492 90 2p e He eU Th Hgg+ -+ -+ �+ �� +D. Acosta Page 3 1/14/2019 + + + + + + Fcoul q Fgrav - - - - - - -PHY2061 Enriched Physics 2 Lecture Notes CoulombCoulomb’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 mq q q qq qx=- >=-=Convention:12Fvdenotes the force acting on particle 1 from the presence of particle 2Since the force is repulsive (same-sign electric charges), 12 12ˆF=-F xv (points in negative x direction). 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=- =F F xv v (points in positive x direction).Again, use this line of reasoning to determine the direction of the force and not the sign inCoulomb’s Law.The magnitude of the force is given by Coulomb’s Law:21 212 122| || || | 3q qF K Kqx= = =FSince 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 forcebetween 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.Find r such that all charges remain at rest, and determine q3 - 2
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