and q Electric Potential A distance r from a charge q is given by V is the test charge and q U V
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1 SPH4 nit 7.4 lectic Potential Page of Notes Physics Tool box lectic Potential negy the electic potential enegy stoed in a syste kqq of two chages q and q is k oulobs onstant is 4 N kq lectic Potential A distance fo a chage q is given by q whee q is the test chage and q is the chage ceating the electic field. This is easued in volts. oltage a coon te fo electic potential : volt is the electic potential at a point in an electic field if J of wok is equied to ove of chage fo infinity to that point: J. The Potential Diffeence between two points in an electic field is given by the change in the electic potential enegy of a positive chage as it oves fo one point to anothe:. q The agnitude of the electic field is the change in potential diffeence pe unit adius: Hee we ae going to talk about enegy associated with electical inteactions. vey tie you tun on an electical appliance, you ae aking use of electical enegy. We ae aleady failia with the concepts of wok and enegy in the context of echanics; now we will cobine these concepts with what we have leaned about electic chages, electic foce, and electic fields. When a chaged paticle oves in an electic field, the field exets a foce that can do wok on the paticle. This wok can always be expessed in tes of electic potential enegy. Just as gavitational potential enegy depends on the height of the ass above the ath s suface, electic potential enegy depends upon the position of the chaged paticle in the electic field. Recall: The agnitude of the foce of gavity between two asses is given by: G FG
2 SPH4 nit 7.4 lectic Potential Page of The gavitational potential enegy between two asses is given by: G G Now conside a sall test chage q, a distance fo a point chage q. Fo oulob s Law, the agnitude of the foce of attaction o epulsion between these two chages is: F kq q Theefoe, it sees easonable that an appoach siila to what we did in the pevious note that the following would be the esult fo electic potential enegy: G kq q Note: the is no negative sign on the potential enegy equation since it could be positive o negative. If both chages have sae sign (ie epel) then the potential enegy will be positive. If the chages have opposite signs (ie will attaction) then the potential enegy will be negative. We see that Potential enegy inceases as opposite chages ecede, and that Potential enegy inceases as like chages appoach. lectic potential o voltage is the diffeence in potential enegy of a chage that oves fo one point in an electic field to anothe. lectic potential is siila to height in gavity pobles. At the sae height above ath s suface, the potential enegy of all objects is conveted to kinetic enegy to poduce the sae final speed. The objects actual enegy value depends on its ass. Siilaly, a chage gains enegy by oving in a electic field though a given voltage diffeence. The aount of enegy it gains depends on how uch chage it has.
3 SPH4 nit 7.4 lectic Potential Page 3 of Regadless of the actual path taken by the chage q 0 in oving a to b. Note: the diffeence between the wok-pe-unit-chage that the electic potential we would pefo in oving ou at b and the electic hypothetical positive test chage potential at a fo a to b in the electic field is usually witten as ba q q 0 b 0 a 0 0 q b q a Fo a point chage q 0, the electic potential diffeence between point b and a can be found by subtacting the electic potentials due to the chage at each position. kq kq 0 0 ba b a kq0 b a b a Now ultiplying by the chage that is oved fo a to b gives us the change in electic potential. q Fo a given position of the test chage in the field, the chage field syste has a potential enegy elative to the configuation of the syste that is defined as = 0. Dividing this potential enegy,, by the value of the test chage, q o gives a physical quantity that depends only on the souce chage distibution. The potential enegy pe unit chage q is independent of the value of q 0 and has a value at evey point in an electic field. This Quantity is called the electic potential (o siply the potential). q o o
4 SPH4 nit 7.4 lectic Potential Page 4 of Thus, the electic potential at any point in an electic field is: q o The fact that potential enegy is a scala quantity eans that electic potential also is a scala. If the test chage is oved between two positions A and B in an electic field, the chage field syste expeiences a change in potential enegy. The potential diffeence between two points A and B in an electic field is defined as the change in B A potential enegy of the syste when a test chage is oved between the points divided by the test chage q 0 : B d s q A o Just as with potential enegy, only diffeences in electic potential ae eaningful. To avoid having to wok with potential diffeences, howeve, we often take the value of the electic potential to be zeo at soe convenient point in an electic field. Potential diffeence should not be confused with diffeence in potential enegy. The potential diffeence between A and B depends only on the souce chage distibution (conside points A and B without the pesence of the test chage), while the diffeence in potential enegy exists only if a test chage is oved between the points. lectic potential is a scala chaacteistic of an electic field, independent of any chages that ay be placed in the field. Note: The potential is chaacteistic of the field only, independent of a chaged test paticle that ay be placed in the field. Potential enegy is chaacteistic of the chage field syste due to an inteaction between the field and a chaged paticle placed in the field. Typically we use vaiety of phases to descibe the potential diffeence between two points, the ost coon being voltage, aising fo the unit fo potential. A voltage applied to a device, such as a copute, o acoss a device is the sae as the potential diffeence acoss the device. If we say that the voltage applied to a copute is volts, we ean that the potential diffeence between the two electical contacts on the copute is volts.
5 SPH4 nit 7.4 lectic Potential Page 5 of opaison of lectic Potential negy and lectic Potential In ode to bing two like chages (positive and positive o negative and negative) nea each othe wok ust be done. Wheneve wok gets done, enegy changes fo. When the one chage is bought close to the othe chage, a positive aount of wok would be done by you. This wok would incease the electical potential enegy of the syste. The foula fo electic potential enegy is: G kq q Since the electical potential enegy can change depending on the aount of chage you ae oving, it is useful to descibe the electical potential enegy pe unit of chage. This is known as electical potential NOT: the nae sounds vey siila to electical potential enegy, but the ole is diffeent. Wok done on Paticle lectic Potential negy lectic Potential = nit of hage Moved nit of hage Moved The foula is usually witten as: W kqnot oved with units of J o olt q oved Fo xaple: e e e + You do 30J of wok to pull apat 3 positive chages ( coulob each) fo a negative chage. This aount of wok inceases the electic potential enegy of the 3 positive chages (these chages etain 30J woth of lectic Potential negy). The electic potential (not enegy) is the aount of enegy pe nit hage. W 30J J 0 0 olts q 3 oved At the oiginal position, when the 3 positive chages ae next to the negative chage, the chages they have no potential enegy, so they also have no electical potential o in othe wods =0 volts. But, once they ae pulled apat, they then have an electical potential of 0 volts. You should notice that the electical potential diffeence fo the one point to the othe is 0 volts. Reebe that the electical potential descibes the aount of enegy pe unit of chage. This eans that if you elease one of the chages then the electic field will do 0 Joules of wok on the chage so it will have a kinetic enegy of 0 Joules the instant befoe it stikes the negative chage. In you wold of expeience, A 9 olt battey indicates that evey oulob ) of chage that oves fo the negative side of the battey to the positive side will do 9 Joules woth of wok.
6 SPH4 nit 7.4 lectic Potential Page 6 of lectic Plates The incease in electic potential enegy of the chage q, in oving fo plate B to plate A, is equal to the wok done in oving it fo B to A. To do so, a foce F, equal in agnitude but opposite in diection to F, ust be applied ove a distance. The agnitude of the wok done is: W q W q F F q q q Potential negy question 9 alculate the closest distance an alpha paticle with chage 3. 0 gets to a gold 7 3 nucleus with chage.6 0 if the alpha paticle has 6. 0 J of kinetic enegy. This question involves the law of consevation of enegy. All of the alpha paticle s kinetic enegy is conveted to potential enegy by the tie it is stopped by the epulsive foce between the two positive chages Ti Tf ki i kf f 3 kqq 6.0 J 0J 0J kqq J N J The closest distance is
7 SPH4 nit 7.4 lectic Potential Page 7 of Potential diffeence Question The potential diffeence between Positive chage plate A and negative chaged plate B is 40. a) Which plate is at the highe potential? b) How uch wok ust be done to cay a 3.0 chage fo B to A c) How uch wok ust be done to cay a 3.0 chage fo A to b d) How do we know that the electic field goes fo A to B e) If the plate sepaation is 5.0, what is the agnitude of the electic field? a) A positive test chage between the plates is epelled by A and attacted by B. Left to itself, the positive test chage will ove fo A to b, and so A is at the highe potential. b) The agnitude of the wok done in caying a chage q though a potential diffeence is W=q W q J Because a positive chage between the plates is epelled by A, positive wok (+0J) ust be done to dag the +3.0 chage fo B to A. c) Since the +3.0 chage will want to ove fo A to B, then -0J of wok is done oving it fo A to B. d) A positive test chage between the plates expeiences a foce diected fo A to B and this is, by definition, the diection of the field. e) Fo paallel plates : The agnitude of the electic field stength is 8000 / o 8000 N/ (ecall that the SI units fo electic field / and N/ ae identical)
8 SPH4 nit 7.4 lectic Potential Page 8 of lectic Potential Poble alculate the electic potential a distance of 0.50 fo a spheical point chage of (take =0 at infinity) kq N The electic potential is Wok Poble How uch wok ust be done to incease the potential of a chage by 00? W q J Wok Poble Find the speed of a ass of and has a chage of kg if it oves though a potential diffeence of 40.0 The equation W q gives you the enegy the chage gains in the fo of kinetic enegy. Theefoe we can substitute v fo W and solve fo the speed.
9 SPH4 nit 7.4 lectic Potential Page 9 of v W q v q q v q 6 c s 6 kg The speed of the ass is theefoe /s. xaple The electic potential diffeence between the inside and outside of a neuon cell ebane of thickness 5.0 n is typically a) xplain why the inne and oute sufaces of the ebane can be thought of as opposite chaged paallel plates b) alculate the agnitude of the electic field in the ebanes. 9 c) alculate the wok you would have to do on a single sodiu ion, of chage.6 0, to ove it though the ebane fo the egion of lowe potential into the egion of highe potential. a) Look at figue 3 on page 356. You notice a positively laye of extacellula fluid paallel to a negatively chaged laye of intacellula fluid. These two paallel layes ae sepaated by a cell ebane given the appeaance of a set of paallel plates. b) Since we ae assuing the sufaces ae acting as paallel plates. Then d N.40
10 SPH4 nit 7.4 lectic Potential Page 0 of c) If the electical foce oves a chage a cetain distance, it does wok on that chage. The change in electic potential ove this distance is defined though the wok done by this foce: Wok done = (Foce) x (distance) = (Potential diffeence) x (hage) W q J
11 SPH4 nit 7.4 lectic Potential Page of xta Notes and oents
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