Electric Charge and Electrostatic Force

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Derek Bennett
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1 PHY 049 Lecture Notes Chapter : Page 1 of 8 Electric Charge an Electrostatic Force Contemporary vision: all forces of nature can be viewe as interaction between "charges", specific funamental properties of matter. Electrostatic force: By rubbing amber against fur, one can iscover that both amber an fur acuire some new properties that cause them attract each other. The new property that is responsible for this force is calle electric charge. What is interesting is that if one splits this way charge amber piece apart, the smaller pieces repel each other. Both facts can be eplaine if one assumes that there are two ins of charges: positive an negative we chose to call them positive an negative; we coul chose "sour" an "sweet", "left" an "right", "ay-lie" an "night-lie" an this woul o just as well same-in charges repel each other opposite ins attract each other

2 PHY 049 Lecture Notes Chapter : Page of 8 Electric Charge an Electrostatic Force SI Units for charge: C, Coulomb we will iscuss later how this unit was chosen--it was erive from units of current 1 C is a very large charge (just try to hol two 1 C charges in your hans!) More on electric charges: total electric charge is conserve, i.e. the net charge in any close system never changes Millien: there is a smallest unit of charge e C Coulomb's Law for point-lie charges: 1 the force is irecte along the line connecting the charges two point charges repel or attract each other (same sign charges repel, opposite sign--attract) the magnitue of the force is as follows: F r = 1 = 1 1 4πε N m /C N m /C = 1/(4πε 0 ), where ε C /(N m ) 0

3 PHY 049 Lecture Notes Chapter : Page 3 of 8 Other "Charges" an Forces in Nature - I Gravitational force: responsible for attraction of planets to the Sun, for an apple falling own, etc., etc. m1 m F = G Here masses m 1 an m are gravitational "charges". There is only one in of gravitational charges--one may want to call them "positive" (any other name woul be as goo). As far as we now mass oes not uantize, i.e. there is no smallest uantum of mass Mass is not conserve, it can be converte into energy: E=mc Gravitational force is very wea, incomprehensibly weaer than electrostatic force (in the worl of elementary particles): Tae eample of two electrons: electrons have mass m e g an charge e = -e C G = Nm /g, = Nm /C me me FG = G e e e FE = = m 43 FG / FE = G / 10 e : Incomprehensibly small number!!!! 1 sec an age of Universe: 1 s / ( years s/year ) (smallest istance we can resolve) / (observable universe) ~ (10-16 m)/(10 m)

4 PHY 049 Lecture Notes Chapter : Page 4 of 8 Other "Charges" an Forces in Nature - II Strong force: responsible for holing protons an neutrons insie an atom nucleus (protons repel each other, while gravitational force is too wee to hol them together). There is si ins of strong force charges--we chose to call them "green", "re", "blue", "anti-green", "anti-re", "anti-blue") For eample: protons, although color-neutral themselves, consist of three uars that carry these charges: proton anti-proton π-meson What about magnetic force?: Once thought to be one of the funamental forces. Now we now it is ue to the same electric charges set in motion

5 PHY 049 Lecture Notes Chapter : Page 5 of 8 Electrostatic Force is a Vector Electrostatic Force is a vector (as any other force). F 1 Q 1 Q F 1 F 3 3 Here are a few tips how to raw the vector forces (accurate rawing is the ey to hanling vector forces): remember that forces act on charges to figure out the force acting on charge in presence of other charges, one nees to jump on charge an count all charges aroun (three in the eample above: Q 1, Q, Q 3 ) Each of these eternal charges will eert a force on charge accoring to the Coulomb 's Law an you raw all three vectors of the forces F i, eperience by the charge a) starting from the point corresponing to charge ; b) along the line connecting an Q i ; c) in irection of attraction/repulsion accoring to signs of charges an Q I ; ) an with magnitue calculate accoring to Coulomb's Law: F = Q i i i The net force acting on charge is the vector sum of all these three forces: F = F 1 + F +F 3 Q 3

6 PHY 049 Lecture Notes Chapter : Page 6 of 8 Graphical Aition of Vectors: Vectors & Vector Aition C = A + B y-ais B C A -ais Breaing a Vectors into - an y-components: y-ais Ay =A sin θ A θ A =A cos θ -ais To a vectors you a the components of the vectors as follows: r A= A iˆ + A ˆ y j + A ˆ z r B = B iˆ + B ˆ y j + Bzˆ r r r C = A+ B = ( A + B )ˆ i + ( A + B )ˆj + ( A y y z + B ) ˆ z

7 PHY 049 Lecture Notes Chapter : Page 7 of 8 Useful Approimations For any small ε ( ε <<1), the following epressions can be approimate as: ( ) p 1 + ε 1+ pε e ε 1+ ε sin ε ε tan ε ε cosε 1 ε

8 PHY 049 Lecture Notes Chapter : Page 8 of 8 Electric Dipole -Q +Q An electric ipole is two eual an opposite point charges separate by a istance. It is an electrically neutral system. The "ipole moment" p is efine to be the charge Q times the separation, i.e., p = Q. Eample Problems: 1. A ipole with charge Q an separation is locate on the y-ais with its mipoint at the origin. A charge is on the -ais a istance from the mipoint of the ipole. What is the electric force on ue to the ipole (assume >>)? +Q -Q ( Q ) F 3. Same, but with the ipole oriente along -ais. +Q -Q ( Q F 3 ) 3. Fin the force between two ipoles oriente as shown: +Q -Q +Q -Q ( Q F 6 4 ) Note that espite the fact that both ipoles are neutral, there remains a resiual wee force between them (~1/ 4 ). Does it contraict to Coulomb's Law? No, the law is formulate for point-lie charges, while ipoles are clearly not point-lie an have internal structure. This problem is intene to help unerstan how neutral atoms can attract each other to mae molecules an form soli objects.

5.4 Fundamental Theorem of Calculus Calculus. Do you remember the Fundamental Theorem of Algebra? Just thought I'd ask

5.4 FUNDAMENTAL THEOREM OF CALCULUS Do you remember the Funamental Theorem of Algebra? Just thought I' ask The Funamental Theorem of Calculus has two parts. These two parts tie together the concept of