Chapter 22 : Electric Potential

Chapter 22 : Electric potential What is electric potential? How does it relate topotential energy? How does it relate toelectric field? Some simple applications

Electric potential What does it meanwhen it says “1.5 Volts”on the battery? The electric potentialdifference between theends is 1.5 Volts

Electric potential230 V1.5 V100,000 VSo what is a volt?

Electric potential The electric potential difference 𝑉𝑉 in voltsbetween two points is the work in Joules needed tomove 1 C of charge between those points𝑊𝑊 𝑞𝑞 𝑉𝑉W work done [in J]q charge [in C] V potential difference [in V] 𝑉𝑉 is measured in volts [V] : 1 V 1 J/C

Electric potential The electric potential difference 𝑉𝑉 in voltsbetween two points is the work in Joules needed tomove 1 C of charge between those points𝑊𝑊 𝑞𝑞 𝑉𝑉The 1.5 V battery does1.5 J of work for every1 C of charge flowinground the circuit

Potential energy What is this thing called “potential”? Potential energy crops up everywhere in physics

Potential energy Potential energy U is the energy stored in a system(when work is done against a force) e.g. force of gravity 𝐹𝐹 𝑚𝑚𝑚𝑚Work Force x Distance𝐹𝐹ℎ𝑊𝑊 𝐹𝐹 ℎ 𝑚𝑚𝑚𝑚𝑚 𝑈𝑈 𝑚𝑚𝑚𝑚𝑚

Potential energy Potential energy may be released and convertedinto other forms (such as kinetic energy)Work is done,increasing thepotential energy

Potential energy Potential energy difference is the only thing thatmatters – not the reference (or zero) level For example, applying conservation of energy to amechanics problem:Final energy Initial 𝑓𝑓𝑓 ��𝑓 ��𝑖𝑖𝑖𝑖𝑖 𝑓𝑓𝑓𝑓𝑓𝑓𝑓 ��𝑖𝑖𝑖𝑖𝑖 ���𝑖𝑖𝑖𝑖𝑖 ��𝑓 )Difference in potential energy

Potential energy Potential energy difference doesn’t depend on thepath – only on the two points A and B

Potential energy Potential energy U is the energy stored in a system– second example e.g. stretching a spring 𝐹𝐹 𝑘𝑘𝑘𝑘Work Force x Distance𝐹𝐹𝑥𝑥Force is varying with distance!𝑊𝑊 𝑘𝑘𝑘𝑘 𝑑𝑑𝑑𝑑 12𝑘𝑘𝑥𝑥 2 𝑈𝑈 12𝑘𝑘𝑥𝑥 2

Electric potential e.g. moving a charge through an electric field 𝐸𝐸𝑞𝑞 𝑥𝑥𝐹𝐹Work Force x Distance𝐹𝐹 𝑞𝑞𝑞𝑞(minus sign because theforce is opposite to E)𝑊𝑊 𝐹𝐹 𝑥𝑥 𝑞𝑞𝑞𝑞 𝑥𝑥 Potential difference 𝑉𝑉 is work needed to move1C of charge: 𝑊𝑊 𝑞𝑞 𝑉𝑉 Equate: 𝑞𝑞 𝑉𝑉 𝑞𝑞𝑞𝑞 𝑥𝑥 𝑉𝑉𝐸𝐸 𝑥𝑥

Electric potential Electric field is the gradient of potential 𝐸𝐸 High V𝐸𝐸Low V𝑉𝑉 𝑉𝑉 𝑥𝑥𝑥𝑥 Positive charges feel a forcefrom high to low potential𝑥𝑥 Negative charges feel a forcefrom low to high potential

Two parallel plates haveequal and opposite charge.Rank the indicated positionsfrom highest to lowestelectric potential.1.2.3.4.A C, B DA, B, C, DC, D B, AA, B D, C- - - - - - - - - - - - A B DC 0%10%20%30%4

Electric potential Analogy with gravitational potentialGravitationalpotential differenceexerts force on massElectric potentialdifference exertsforce on charge𝑉𝑉𝑞𝑞𝑥𝑥

Electric potential Electric field is the gradient of potential 𝐸𝐸 High V𝐸𝐸Low V 𝑉𝑉 𝑥𝑥 The dashed lines are calledequipotentials (lines ofconstant V) Electric field lines areperpendicular to equipotentials It takes no work to move acharge along an equipotential⃗ 𝑑𝑑𝑑𝑑 (work done 𝑑𝑑𝑑𝑑 𝐹𝐹.𝑞𝑞𝐸𝐸. 𝑑𝑑𝑑𝑑 0)

Electric potential Summary for two plates at potential difference V𝐸𝐸 Electric field is the potentialgradient𝑉𝑉𝐸𝐸 𝑑𝑑 Work W to move charge qfrom –ve to ve plate𝑑𝑑𝑊𝑊 𝑞𝑞 𝑉𝑉

Link to potential energy The electric potential difference 𝑉𝑉 between twopoints is the work needed to move 1 C of chargebetween those points𝑊𝑊 𝑞𝑞 𝑉𝑉 This work is also equal to the potential energydifference 𝑈𝑈 between those points 𝑈𝑈 𝑞𝑞 𝑉𝑉 Potential V potential energy per unit charge U/q

An electron is placed at “X” on thenegative plate of a pair of chargedparallel plates. For the maximumwork to be done on it, which pointshould it be moved to?1.2.3.4.5.6.ABCDA or CC or D- - - - - - - - - - - - DX BAC 0%0%120%0%0%0%3456

Electric potential What is the electric potential near a charge Q?Work Force x Distance𝑘𝑘 𝑄𝑄 𝑞𝑞𝐹𝐹 2𝑥𝑥 q𝑥𝑥Force is varying with distance, need integral!𝑟𝑟𝑟𝑟𝑘𝑘 𝑄𝑄 𝑞𝑞𝑘𝑘 𝑄𝑄 𝑞𝑞𝑊𝑊 𝐹𝐹 𝑑𝑑𝑑𝑑 2 𝑑𝑑𝑑𝑑 𝑥𝑥𝑟𝑟 QPotential energy 𝑈𝑈 Electric potential 𝑉𝑉 𝑈𝑈𝑞𝑞𝑘𝑘 𝑄𝑄 𝑞𝑞𝑟𝑟 𝑘𝑘 𝑄𝑄𝑟𝑟

Electric potential What is the electric potential near a charge Q? q𝑟𝑟 QElectric potential 𝑉𝑉 𝑘𝑘 𝑄𝑄𝑟𝑟

Electric potentialExercise: a potential difference of 200 V is applied across apair of parallel plates 0.012 m apart. (a) calculate E and drawits direction between the plates.The electric field is the gradient in potential200 𝑉𝑉 𝐸𝐸 0.012 𝑥𝑥𝑉𝑉 200𝑉𝑉 0𝐸𝐸 1.7 104 𝑉𝑉 𝑚𝑚 1 [𝑜𝑜𝑜𝑜 𝑁𝑁 𝐶𝐶 1 ] ve plate-ve plate

Electric potentialExercise: a potential difference of 200 V is applied across apair of parallel plates 0.012 m apart. (b) an electron is placedbetween the plates, next to the negative plate. Calculate theforce on the electron, the acceleration of the electron, and thetime it takes to reach the other plate.Force 𝐹𝐹 𝑞𝑞𝑞𝑞 ( 1.6 10 19 ) (1.7 104 ) 2.7 10 15 𝑁𝑁𝐹𝐹 𝑚𝑚𝑚𝑚𝐸𝐸Acceleration 𝑎𝑎 ve plate 𝑒𝑒-ve plate 152.7 10𝐹𝐹 𝑚𝑚9.1 10 31𝑑𝑑 12𝑎𝑎𝑡𝑡 2𝑡𝑡 2 0.0123.0 1015e 1.6 x 10-19 C; me 9.1 x 10-31 kg 3.0 1015 𝑚𝑚 𝑠𝑠 2Time 𝑡𝑡 2𝑑𝑑𝑎𝑎 2.8 10 9 𝑠𝑠

Electric potentialExercise: a potential difference of 200 V is applied across apair of parallel plates 0.012 m apart. (c) calculate the workdone on the electron as it travels between the plates.The potential difference is the work done on 1C chargeWork 𝑊𝑊 𝑞𝑞𝑞𝑞 1.6 10 19 200 3.2 10 17 𝐽𝐽 ve plate𝐸𝐸 𝑒𝑒-ve platee 1.6 x 10-19 C; me 9.1 x 10-31 kg

Chapter 22 summary Electric potential difference V is the work donewhen moving unit charge: 𝑊𝑊 𝑞𝑞𝑞𝑞 The electric potential energy is therefore alsogiven by: 𝑈𝑈 𝑞𝑞𝑞𝑞 The electric field is the gradient of the potential:𝐸𝐸 𝑉𝑉/ 𝑥𝑥 Charges feel a force from high electric potentialto low potential

Potential energy may be released and converted into other forms (such as kinetic energy) Work is done, increasing the potential energy. Potential energy Potential energy difference is the on