17.1 Electric Potential Energy. Equipotential Lines. PE = energy associated with an arrangement of objects that exert forces on each other

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Electic Potential Enegy, PE Units: Joules Electic Potential, Units: olts 17.

chages PE = enegy associated with an aangement of objects that exet foces on each othe PE = capacity o potential to do wok Why does lightning occu?

potential diffeence, ba PE ba = q ba Electic Potential Electic Potential (Electic) Potential, a is a scala quantity that is associated with the chages that ceate the E field a is defined to be the

1 Electic Potential Enegy, PE Units: Joules Electic Potential, Units: olts 17.1 Electic Potential Enegy Electic foce is a consevative foce and so we can assign an electic potential enegy (PE) to the system Equipotential Lines The Electon olt Unifom E field Assembling point chages PE = enegy associated with an aangement of objects that exet foces on each othe PE = capacity o potential to do wok Why does lightning occu? apacitance Dielectics Stoage of Electic Enegy hange in Gavitational PE fo a mass, m, nea the Eath s suface PE gavity = mgh hange in Electic PE fo a chage, q, that moves fom point a to b though a potential diffeence, ba PE ba = q ba Electic Potential Electic Potential (Electic) Potential, a is a scala quantity that is associated with the chages that ceate the E field a is defined to be the electic potential enegy pe unit chage Units = volts 1 = 1 J/ Potential at a Potential enegy of system small (positive) test chage placed at point a (17-2a) a depends only on the chages that ceate the E field not the test chage, q. In the eal wold only changes in PE ae physically meaningful, so ewite 17.2a in tems of the potential diffeence. Potential diffeence o ꞌoltageꞌ = change in the PE pe unit chage We define whee =0 = Units: volt () 1 = 1 J/. (=0 at the gound in a cicuit which is typically located at the negative teminal of the battey Fo a collection of point chages, = 0 at = ) (17-3) So, what does the electic potential () look like? PE ba = q ba q -Q Electic Potential It s a scala (a numbe) so poblem solving is easie than with electic fields (vectos) - but take cae with the sign of the potential. Think of potential as a topological map is like height and q is like mass in the gavitational case PE G = mgh m is HIGH nea (+) chages and LOW nea (-) chages And we typically take = 0 at = h Potential at a distance fom a point chage Q is given by, Fo a positive pt. chage Electic Potential (deived using calculus and assuming = 0 at = ). [point chage] (17-5).. and a negative chage. -Q Note, this fomula gives the potential at AND the potential diffeence between and 1

2 17.3 Equipotentials 17.3 Equipotentials We can epesent the potential nea a point chage, Q using spheical equipotentials 10 0 infinitely fa away fom Q Fo a collection of point chages, simply add the potentials fom the individual chages E field is stongest whee the equipotentials ae close All points on an Equipotential line o suface ae at the same potential Equipotentials and Field lines fo a dipole (equal and opposite point chages) E field lines ae to Equipotentials What is the potential at the cente of the squae? (assume = 0 vey fa fom the chages) 17.3 Equipotentials In a capacito, the potential changes linealy fom one plate to the othe. - Q l + Q Equipotentials ae equally spaced planes, paallel to the capacito plates. The suface of a conducto is an equipotential. - Q + Q l Is E = 0 at the cente too? Equipotentials and Field lines between two capacito plates Electic field lines ae pependicula to equipotentials. an the equipotentials be evesed (0 20) in the figue? Remembe Potential is highe at the positive plate Potential and Potential Enegy ae diffeent! [olts] Look at the apacito again We choose whee = 0. Potential at a point is a scale (numbe) that depends on the chage on the plates and whee we define zeo volts to be. [Joules] high PE q + q - low PE low PE high PE = Potential enegy of the system when point chage, q is at point a, depends on the potential and q. What is the change in PE when it eaches the negative plate? J J 3. No change 4. Infinite A + 4 point chage stats fom est and moves fom a to b What if it wee a negative 4 chage? 4 point chage a b 5 The + 4 chage has a mass of 1x10-3 kg. How fast is it going when it eaches b? 1. 4 m/s m/s 3. 40,000 m/s 4. ey close to the speed of light 2

17.4 The Electon olt - a Unit of Enegy In atoms, 1 Joule is a ERY lage amount of enegy so we often use a diffeent unit: The electonvolt, e (13 cm ~ 390,000) One e = enegy acquied by a paticle with

A 1 cm spak coesponds to a potential diffeence of 30,000 Eg: How much KE does an electon gain when it is acceleated fom est though a potential diffeence of 250?

Wok The wok done by the electic foce (W ba ) on a chage q as it moves in an electic field is defined to be minus the change in the electic potential enegy W ba = - PE ba = - q ba Units = Joules (17.

wok (Phys 111: = + ) use this if KE 0 E How much wok is done by an extenal foce to move a 1 chage fom.. A B? B? A? The next thee slides have been updated. I emoved the deivation of equation 17-4a 17.

3 17.4 The Electon olt - a Unit of Enegy In atoms, 1 Joule is a ERY lage amount of enegy so we often use a diffeent unit: The electonvolt, e (13 cm ~ 390,000) One e = enegy acquied by a paticle with chage of magnitude e when it moves though a potential diffeence of 1 volt. A 1 cm spak coesponds to a potential diffeence of 30,000 Eg: How much KE does an electon gain when it is acceleated fom est though a potential diffeence of 250? e 250 It gains 250 e of KE and loses 250 e of PE (enegy consevation). Wok The wok done by the electic foce (W ba ) on a chage q as it moves in an electic field is defined to be minus the change in the electic potential enegy W ba = - PE ba = - q ba Units = Joules (17.2b ) q a b E PE ba = PE b PE a 5 A B (assume KE = 0) The wok done by an extenal foce in moving a chage q in an electic field is Note the W ext = q ba a b (only if KE=0) diffeent sign fo extenal wok (Phys 111: = + ) use this if KE 0 E How much wok is done by an extenal foce to move a 1 chage fom.. A B? B? A? The next thee slides have been updated. I emoved the deivation of equation 17-4a 17.2 Relation between electic potential and field How does E elate to? The component of E in a given diection is equal to the ate at which the electic potential deceases ove distance in that diection New units fo = [geneal E] electic field: /m E points in diection of deceasing So fo the unifom electic field inside a capacito E inside a capacito is equal to minus the potential diffeence between the plates divided by the plate sepaation = [unifom E] (17-4a) What is the electic field inside a capacito if one plate is at +12 and the othe plate is at -3? The plates ae sepaated by 2 mm. 2 mm The potential is 20 eveywhee in this egion What is E in this egion? 3

Example: Wok equied to assemble a numbe of point chages Example: Wok equied to assemble a numbe of point chages + (let KE = 0) = 0 at = Q 1 + - To calculate the extenal wok equied to assemble seveal

Thee ae no othe chages pesent so ba = 0, and W ext = 0 (assume =0) Use the above eqn.

Potential diffeence (due to Q 1 ) between infinity and, is Q Q 2 1 1 1 (17-5) Q 1 Q 2 13 23 Wok done by extenal foce to move Q 2 is W ext = Q 2 1 = Q 2 kq 1 Wok done by an extenal foce in moving Q 3

Total wok needed to assemble the chages is the sum of all steps What can you say about the wok done by an EXTERNAL FORE to bing a +1 µ chage fom fa away and place it on the thid cone of the

4 Example: Wok equied to assemble a numbe of point chages Example: Wok equied to assemble a numbe of point chages + (let KE = 0) = 0 at = Q To calculate the extenal wok equied to assemble seveal point chages use W ext = q ba How much wok is done by an extenal foce to bing chage Q 1 fom infinity and place it at the oigin? Zeo! Thee ae no othe chages pesent so ba = 0, and W ext = 0 (assume =0) Use the above eqn. and bing the chages in fom infinity one at a time How much wok is done by an extenal foce to bing a 2 nd chage (Q 2 ) fom infinity and place it a distance fom Q 1? Potential diffeence (due to Q 1 ) between infinity and, is Q Q (17-5) Q 1 Q Wok done by extenal foce to move Q 2 is W ext = Q 2 1 = Q 2 kq 1 Wok done by an extenal foce in moving Q 3 is, W ext = Q Q 3 = Q 3 kq 1 + Q 3 kq = Q 3 ( ) Fo moe chages, just add moe tems. Total wok needed to assemble the chages is the sum of all steps What can you say about the wok done by an EXTERNAL FORE to bing a +1 µ chage fom fa away and place it on the thid cone of the equilateal tiangle? 1. Its positive + 1 µ 2. Its negative d d 3. Its zeo + 1 µ - 1 µ d 4. Huh? 17.7 apacitance A capacito consists of two conductos that ae close but not touching. How much WORK is done by the ELETRI FORE when the 2.0 µ chage moves close to the positive chage, as shown? 2.0 µ 10.0 cm 4.0 cm µ (the + 3 µ chage is fixed in space) apacito symbol (1) 0 J (2) J (3) J (4) J What does a capacito do? 17.7 apacitance 17.8 Dielectics Fo a chaged capacito.. chage on each plate voltage acoss capacito (17-7) A dielectic is an insulato, chaacteized by a dielectic constant K. Units: faad (F) 1 F = 1 / apacitance depends on geomety and capacito mateials. apacitance of a paallel-plate capacito INREASES when it is filled with a dielectic: cicuit diagam Fo a paallel-plate capacito (with ai gap) (17-8) Pemittivity of fee space 8.85 x /Nm 2 d ε = pemittivity of the mateial = K ε 0 A/d ε = K ε 0 (17-9) Max field a dielectic can expeience without beaking down. 4

on it? + Q - Q 1. Q stays constant, deceases, deceases 2. Q stays constant, deceases, inceases 3. Q stays constant, inceases, deceases 4. Q stays constant, inceases, inceases 5.

5 17.8 Dielectics 17.9 Stoage of Electic Enegy Eg: What happens when a dielectic is inseted into a capacito connected to a battey? stays constant (battey keeps constant) inceases (due to dielectic) Q inceases (Q =, moe chage is pulled fom battey) What happens when a dielectic is inseted into an isolated capacito that has chage Q on it? + Q - Q 1. Q stays constant, deceases, deceases 2. Q stays constant, deceases, inceases 3. Q stays constant, inceases, deceases 4. Q stays constant, inceases, inceases 5. Q inceases, stays constant, inceases A chaged capacito also stoes electic enegy Enegy stoed (PE) = wok done to chage the capacito. (17-10) Enegy density, u E = stoed Units enegy pe unit volume, is the same no matte the u E = J/m 3 oigin of the electic field: (17-11)... A chaged paallel-plate capacito is disconnected fom a battey. Suppose the capacito plates ae pulled apat. Pointed conductos, ion winds, lightning and St. Elmo s fie In h. 16 we saw that E = 0 inside a conducto and is to the oute suface. In non-spheical conductos, suface chage densities and electic fields ae biggest whee the cuvatue is geatest. Equipotentials ae close togethe thee too. What happens to the potential enegy stoed in the capacito? 1. It inceases 2. It deceases 3. It stays the same Whee does that enegy come fom? conducto Equipotentials (dashed) Big suface chage density and E field Field lines (solid) If the E field is stong enough an ion wind o coona dischage may occu (St. Elmo Fie) Summay of hapte 17 Wok done by electic foce on a chage that moves in electic field is minus change in PE: W ba = - PE hange in potential enegy when a chage q moves though potential diffeence of is, PE = q (17-3) E = - /d Unifom field (17-4a) Potential diffeence between and due to pt. chage Q Point chage (17-5) Equipotential = line o suface at constant potential. hage on a capacito: apacitance of a paallel-plate capacito: A dielectic is an insulato. It can be used to incease the capacitance of a capacito by a facto K. 5

Force and Work: Reminder

Force and Work: Reminder Electic Potential Foce and Wok: Reminde Displacement d a: initial point b: final point Reminde fom Mechanics: Foce F if thee is a foce acting on an object (e.g. electic foce), this foce may do some wok