SPH4UI 28/02/2011. Total energy = K + U is constant! Electric Potential Mr. Burns. GMm

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1 8//11 Electicity has Enegy SPH4I Electic Potential M. Buns To sepaate negative an positive chages fom each othe, wok must be one against the foce of attaction. Theefoe sepeate chages ae in a higheenegy state. When the chages ae bought back togethe again, enegy must be elease. It may be in the fom of a spak. Consie a small test chage in the electic fiel aoun a positive chage object. The fiel is pushing it in the iection of the fiel lines. If some extenal foce pushes it the othe way, against the iection of the fiel, wok is being one on it. Theefoe, a positive chage has its geatest electic potential enegy at the uppe en (closest to chage object) of the fiel. Since the fiel pushes a negative chage the othe way, its potential enegy is geatest at the lowe en. F Review: Gavitational Foce is consevative Consie a comet in a highly elliptical obit () pt 1 pt Electic Potential Enegy We see that potential enegy inceases as opposite chages ecee, an that potential enegy inceases as like chages appoach. t point 1, paticle has a lot of potential enegy, but little kinetic enegy t point, paticle has little potential enegy, but a lot of kinetic enegy ( 1 ) GMm () ( ) Moe potential enegy Less potential enegy Total enegy = K + is constant! 1

2 8//11 Electic Potential Enegy Electic Potential Enegy Electic Potential Enegy: Doesn t it kina look familia? k1 The electostatic foce is a consevative (= path inepenent ) foce It is possible to efine an electical potential enegy function with this foce Wok one by a consevative foce is eual to the negative of the change in potential enegy. Think of the wok one by gavity to aise an object to a highe location, since gavity points own an the isplacement is up, theefoe the wok is negative. Yet, the potential enegy inceases. Electic Foce is consevative Electic Potential - Consie a chage paticle taveling though a egion of static electic fiel: + negative chage is attacte to the fixe positive chage negative chage has moe potential enegy an less kinetic enegy fa fom the fixe positive chage, an moe kinetic enegy an less potential enegy nea the fixe positive chage. But, the total enegy is conseve We will now iscuss electic potential enegy an the electostatic potential. Electic Potential Consie the electic potential enegy not just of any chage, but of a unit positive test chage when in the fiel of any othe chage 1. k1 Recall: Electic Potential Enegy: We call this value of potential enegy pe unit positive chage the electic potential. The units of electic potential ae joules pe coulomb, o volts V k1 1 k1 Electic Potential Enegy chage Electic Potential escibes how much wok is one pe unit chage.

3 8//11 Electic Potential Diffeence High Potential Low Potential Enegy an Chage Movements + Electic Potential Diffeence The amount of wok euie pe unit chage to move a positive chage fom one point to anothe in the pesence of an electic fiel. The units ae also volts V 1 1 k1 b a positive chage gains electical potential enegy when it is move in a iection opposite the electic fiel If a chage is elease in the electic fiel, it expeiences a foce an acceleates, gaining kinetic enegy s it gains kinetic enegy, it loses an eual amount of electical potential enegy negative chage loses electical potential enegy when it moves in the iection opposite the electic fiel Enegy an Chage Movements Summay of Positive Chage Movements an Enegy When the electic fiel is iecte ownwa, point B is at a lowe potential than point positive test chage that moves fom to B loses electic potential enegy It will gain the same amount of kinetic enegy as it loses potential enegy F= When a positive chage is place in an electic fiel It moves in the iection of the fiel It moves fom a point of highe potential to a point of lowe potential Its electical potential enegy eceases Its kinetic enegy inceases 3

4 8//11 Summay of Negative Chage Movements an Enegy When a negative chage is place in an electic fiel It moves opposite to the iection of the fiel It moves fom a point of lowe potential to a point of highe potential It moves fom a point whee it has highe potential enegy to a point whee it has lowe potential enegy. Its electical potential enegy eceases Its kinetic enegy inceases Review of Potential an Potential Enegy Foce: + + Foce: - + Foce: + - Foce: Moves fom High Potential (V) to Low Potential (V) - Potential enegy () eceases - Electic Fiel (E) oes positive wok - Moves fom Low Potential (V) to High Potential (V) - Potential enegy () eceases - Electic Fiel (E) oes positive wok - Moves fom High Potential (V) to Low Potential (V) - Potential enegy () eceases - Electic Fiel (E) oes positive wok - Moves fom Low Potential (V) to High Potential (V) - Potential enegy () eceases - Electic Fiel (E) oes positive wok Electic potential enegy Imagine two positive chages, one with chage Q 1, the othe with chage Q : Q 1 Q Initially the chages ae vey fa apat, so we say that the initial enegy i of inteaction is zeo (we ae fee to efine the enegy zeo somewhee). If we want to push the paticles togethe, this will euie wok (since they want to epel). Q 1 Q the final enegy f of the system will incease by the same amount: = f i = W Electic potential Enegy Peten 1 is fixe at the oigin. you What is the wok euie to move, initially at infinity, to a istance away? FE Q 1 Q R Remembe wok is foce k1times istance: R k1 W F l 1 What if wee negative (but 1 still positive)? R Then the wok euie by us woul be negative the chages woul like to k come 1 togethe. k1 In this case the final enegy is negative! 1 Paticles will move to minimize the final potential enegy. R W F 1 k R k R 4

5 8//11 Electic Potential Enegy In aition to iscussing the enegy of a test chage in a Coulomb fiel, we can speak of the electic potential enegy of the fiel itself! Reasons? Wok ha to be one to assemble the chages (fom infinity) into thei final positions. This wok is the potential enegy of the fiel. The potential enegy of a system of N chages is efine to be the algebaic sum of the potential enegy fo evey pai of chages. This theme continues in the couse with E in capacitos an B in inuctos these evices stoe electic an magnetic enegy. We will stat with a couple of example calculations Electic Potential Enegy - Example 1: What is the potential enegy of this collection of chages? + - Step 1: Bing in + fom infinity. This costs nothing. Step : Bing in one - chage. The foce is attactive! The wok euie is negative: k( )( ) Step 3: Bing in n - chage. It is attacte to the +, but epelle fom the othe - chage. The total wok (all 3 chages) is k( )( ) k( )( ) k( )( ) k 1 4 negative amount of wok was euie to bing these chages fom infinity to whee they ae now (i.e., the attactive foces between the chages ae lage than the epulsive ones). CT 1 Consie the 3 collections of point chages shown below. Which collection has the smallest potential enegy? -Q -Q -Q -Q (a) (b) (c) -Q CT 1 Consie the 3 collections of point chages shown below. Which collection has the smallest potential enegy? -Q -Q -Q -Q (a) (b) (c) -Q We have to o positive wok to assemble the chages in (a) since they all have the same chage an will natually epel each othe. In (b) an (c), it s not clea whethe we have to o positive o negative wok since thee ae attactive pais an one epulsive pai. (a) 3 kq (b) kq (c) kq (b) (c) (a) 5

a) inceases b) eceases c) oesn t change Electic potential Consie that we have thee chages fixe in space.

6 8//11 Electic Potential Two chages which ae eual in magnitue, but opposite in sign ae place at eual istances fom point. If a thi chage is ae to the system an place at point, how oes the electic potential enegy of the chage collection change? a) inceases b) eceases c) oesn t change Electic potential Consie that we have thee chages fixe in space. The potential enegy of an ae test chage at point P is just of at P Q Q Q 1 3 k k k 1 p p 3 p Note that this factos: x (the effects of all othe chages) Just as we peviously efine the electic fiel as the atio of foce/chage, we now efine the electic potential as the potential enegy/chage: V o = V epens on what o is, but V is inepenent of o (can be + o -) nits of electic potential ae volts: 1 V = 1 J/C V is a scala fiel, efine eveywhee in space. Q 1 Q p 1p Q 3 3p Wok an Potential Enegy Wok an Potential Enegy Thee is a unifom fiel between the two plates s the positive chage moves fom to B, wok is one W B =F =( E) Δ =-W B =- E only fo a unifom fiel poton moves fom est in an electic fiel of V/m along the +x axis fo 5 cm. Fin: a) the change in in the electic potential b) the change in the electical potential enegy c) the spee afte it has move 5 cm. V E 4 V V 8.1.5m m V 6

7 8//11 Wok an Potential Enegy b) the change in the electical potential enegy c) the spee afte it has move 5 cm. K K i i f f K K f i 1 mv 6.41 i f 15 J E E V C V v 15 (6.41 J) / m s kg Potential Diffeence (= Voltage Dop ) The potential iffeence (V) between points an B is efine as the change in the potential enegy () (final value minus initial value) of a chage move fom to B ivie by the size of the chage B W V VB V Potential Diffeence is not the same as Potential Enegy Electic potential iffeence, in tems of E Suppose chage is move fom pt to pt B though a egion of space escibe by electic fiel E. B Foce on the chage ue to E wok W B W B will have to be one to accomplish this task: WB VB V To get a positive test chage fom lowe potential to highe potential you nee to invest enegy - you nee to o wok. The oveall sign of this: positive chage woul fall fom a highe potential to a lowe one If a positive chage moves fom high to low potential, it can o wok on you; you o negative wok on the chage. F elec F we supply = -F elec E 7

8//11 Potential Diffeence an a Battey Potential Diffeence an a Battey Electic cicuits ae all about the movement of chage between vaying locations an the coesponing loss an gain of enegy which

Wok must be one on a positive test chage to move it though the battey fom the negative teminal to the positive teminal.

s the positive test chage moves though the extenal cicuit fom the + teminal to the negative teminal, it eceases its electic potential enegy an thus is at low potential by the time it etuns to the

8 8//11 Potential Diffeence an a Battey Potential Diffeence an a Battey Electic cicuits ae all about the movement of chage between vaying locations an the coesponing loss an gain of enegy which accompanies this movement. The concept of electic potential can be applie to a simple battey-powee electic cicuit. Wok must be one on a positive test chage to move it though the battey fom the negative teminal to the positive teminal. This wok woul incease the potential enegy of the chage an thus incease its electic potential. s the positive test chage moves though the extenal cicuit fom the + teminal to the negative teminal, it eceases its electic potential enegy an thus is at low potential by the time it etuns to the negative teminal. If a 1 volt battey is use in the cicuit, then evey coulomb of chage is gaining 1 joules of potential enegy as it moves though the battey. n similaly, evey coulomb of chage loses 1 joules of electic potential enegy as it passes though the extenal cicuit. With a clea unestaning of electic potential iffeence, the ole of a battey in a simple cicuit can be coectly unestoo. The battey simply supplies the enegy to o wok upon the chage to move it fom the negative teminal to the positive teminal. By poviing enegy to the chage, the battey is capable of maintaining an electic potential iffeence acoss the two ens of the extenal cicuit. Once the chage has eache the high potential teminal, it will natually flow though the wies to the low potential Potential iffeence an Enegy Question Potential iffeence an Enegy Question What is the potential iffeence acoss an ai conitione if 7C of chage tansfe 8.5 x 1 3 J of enegy to the fan an compesso? static electic shock elivee to a stuent fom a fien tansfes 15 J of electic enegy though a potential iffeence of 5V. What is the uantity of chage tansfee in the spak? V J 7C 1.1 V V V 15J 5V.3C 18.3C 6.51 e C e 8

9 8//11 Electic potential E Points, B, an C lie in a unifom electic fiel. What is the potential iffeence between points an B? ΔV B = V B - V a) ΔV B > b) ΔV B = c) ΔV B < Point C is at a highe potential than point? Tue B False C Electic potential Question positive chage is elease fom est in a egion of electic fiel. The chage moves: a) towas a egion of smalle electic potential b) along a path of constant electic potential c) towas a egion of geate electic potential Electic potential nestaning Question Electic Potential Diffeence If you want to move in a egion of electic fiel without changing you electic potential enegy. How woul you choose the iection? You woul have to move pepenicula to the fiel if you wish to move without changing electic potential. single chage ( Q = -1mC) is fixe at the oigin. Define point at x = + 5m an point B at x = +m. What is the sign of the potential iffeence between an B? (Δ V B V B - V ) (a) ΔV B < (b) Δ V B = (c) Δ V B > -1mC B The simplest way to get the sign of the potential iffeence is to imagine placing a positive chage at point an etemining which way it woul move. Remembe that a positive chage will always fall to lowe potential. positive chage at woul be attacte to the -1mC chage; theefoe NEGTIVE wok woul be one to move the chage fom to B. x 9

10 8//11 Δ V B is Inepenent of Path Electic potential V V B W B Δ V B is the same fo any path chosen to move fom to B (because electic foces ae consevative). Euipotential lines ae connecte lines of the same potential. These often appea on fiel line iagams. Euipotential lines ae always pepenicula to fiel lines, an theefoe pepenicula to the foce expeience by a chage in the fiel. If a chage moves along an euipotential line, no wok is one; if a chage moves between euipotential lines, wok is one. E B Euipotentials an Electic Fiels Lines (Positive Chage): The euipotentials fo a point chage ae a family of sphees centee on the point chage The fiel lines ae pepenicula to the electic potential at all points Electic potential Question positive chage Q is move fom to B along the path shown by the aow. What is the sign of the wok one to move the chage fom to B? (a) W B < (b) W B = (c) W B > iect calculation of the wok one to move a positive chage fom point to point B is not easy. Neithe the magnitue no the iection of the fiel is constant along the staight line fom to B. But, you DO NOT have to o the iect calculation. Remembe: potential iffeence is INDEPENDENT OF THE PTH!! Theefoe we can take any path we wish. Choose a path along the ac of a cicle centee at the chage. B 1

11 8//11 Electic Potential: Whee is it zeo? Potential fom N chages Define the electic potential of a point in space as the potential iffeence between that point an a efeence point. a goo efeence point is infinity... we often set V = Thus, at a istance fom a spheical point chage, the electic potential is given by: k V The potential fom a collection of N chages is just the algebaic sum of the potential ue to each chage sepaately (this is much easie to calculate than the net electic fiel, which woul be a vecto sum). Q 1 Q 1p Q 3 N N n V ( ) Vn ( ) k n1 n1 n 3p kq1 kq kq3 p Vat P 1 p p 3 p P Voltage +5 μc -3 μc Two chages 1 = + 5 μc, = -3μC ae place at eual istances fom the point. What is the electic potential at point? a) V < b) V = c) V > V at kq1 kq 1p p 5m 3m k C k C R R kmc R The Electon Volt The electon volt (ev) is efine as the enegy that an electon (o poton) gains when acceleate though a potential iffeence of 1 V Electons in nomal atoms have enegies of 1 s of ev Excite electons have enegies of 1 s of ev High enegy gamma ays have enegies of millions of ev 1 V=1 J/C 1 ev = 1.6 x 1-19 J 11

12 8//11 Summay Summay Electic potential enegy Is the enegy of an electically chage paticle In an electic fiel. Define as wok that must be one to move it fom an infinite istance away to its pesent location. Can be positive o negative (same signs then positive, opposite signs then negative) Electic Potential Is the value of the potential enegy pe unit of positive chage in Volts. kq V kq W Summay Summay cts Electic Potential Diffeence Is the amount of wok euie pe unit chage to move a positive chage fom one point to anothe in the pesence of an electic fiel. The electical potential enegy fo each coulomb of chage in a cicuit is calle the electic potential iffeence V 1 1 kq b a How much wok oes it take to move a chage of +3 nanocoulombs though a potential iffeence of 6. volts Solution: We ae given a potential iffeence Theefoe: V We want wok o change in potential enegy V 9 31 C J J C 1

13 8//11 Summay cts Fin the spee of the mass of.5 x 1-6 kg if it moves though a potential iffeence of 3. V an has a chage of 4.1 x 1-6 C. Summay Euations kq F 1 Q 4 (magnitue only) Solution: We euie velocity, theefoe think about enegy (½ mv ). 1 W V mv V m 9.9 s Wok =change kinetic enegy V v m C3.V 6.51 kg F kq E V kq e Q e kq E W V Electic Fiel is a Vecto uantity (N/C) Potential enegy Chage ensity fo paallel plates. Electic potential: Whee is the test chage an Q is the chage ceating the fiel Wok one Summay Euations ne V E o E E E 4 Q E E enclose Q C V C C C, C C C o n is the numbe of electons Fo paallel plates Total flux close cicle ny enclose suface Electic fiel of cyline at a istance fom cente, Is chage ensity. Capacitance of capacito In seies, in paallel 1 Flash Electic Potential 13

4. Compare the electric force holding the electron in orbit ( r = 0.53

4. Compare the electric force holding the electron in orbit ( r = 0.53 Electostatics WS Electic Foce an Fiel. Calculate the magnitue of the foce between two 3.60-µ C point chages 9.3 cm apat.. How many electons make up a chage of 30.0 µ C? 3. Two chage ust paticles exet a