Chapter Seenteen: Electric Potential and Electric Energy Key Ter Electric Potential electrical potential energy per unit charge (JC -1 ) Page 1 of Electrical Potential Difference between two points is easured by the work required to oe a unit of electric charge between these two points (olts) Equipotential Lines are lines along which each point is at the sae potential. On an equipotential surface, each point on the surface is at the sae potential. Volt is the coon ter for potential difference (1V 1JC -1 ) electron Volt (ev) Electric Potential is the unit for the energy gained by an electron which is accelerated through a potential difference of one olt (1eV 1. J). Work is done when a force oes soething in the direction of the force. An object has potential energy by irtue of its location (in a force field). Work Graity Electric done field field aerage Work Work Increase in potential energy. force distance (g) h (qe) d Electric Potential (or ore siply Potential) Note: V V electric qe d q potential charge Ed energy unit (Volt) or Joule/Coulob ie 1V1JC -1 higher potential is at the positie plate W (Work) qed Vq so E V/d (Volts/etre) since V Ed Physics, 5 th Edition Chapter Seenteen: Electric Potential and Electric Energy
Electron in TV Tube (This coes directly fro Exaple 1- in Giancoli) Suppose an electron in the picture tube of a teleision set is accelerated fro rest through a potential difference V +5.0 V. Page of (a) What is the change in potential energy of the electron? The charge on an electron is e-1. C. Therefore its change in potential energy is equal to: 19 1 ( 1. C)( + 5 V) 8 0 J PE qv. The inus sign in the result indicates that the PE decreases. (The potential difference, V, has a positie sign since the final potential is higher than the initial potential; that is, negatie electrons are attracted fro a negatie electrode to a positie one). (b) What is the speed of the electron (ass 9.1-1 kg) as a result of this acceleration? The potential energy lost by the electron becoes kinetic energy. Fro conseration of energy, KE + PE 0, so KE PE 1 0 qv where the initial KE0 since we assue the electron started fro rest. We sole for and put in the ass of the electron 9.1-1 kg: qv 4. 7 1 (-1. C)( 5 V) 1 ( 9. 1 kg ) (Note: For such a high speed, which is 1 / 7 the speed of light, we should use the theory of relatiity). Physics, 5 th Edition Chapter Seenteen: Electric Potential and Electric Energy
(c) Repeat for a proton (1.7-7 kg) that accelerates through a potential difference of V -5.0 V. The proton has the sae agnitude of charge as the electron, though of opposite sign. Hence for the sae agnitude of V we expect the sae change in PE, but a lesser speed since the proton s ass is greater. Thus: Page of PE qv 19 1 ( + 1. C )( 5 V ) 8. 0 J and qv 9. 8 5 1 (- 1. C )( 5 V ) 7 ( 1. 7 kg ) Note that the energy doesn t depend on the ass, only on the charge and oltage. The speed does depend on ass. Equipotential Lines The electric potential can be represented diagraatically by drawing equipotential lines. Note: All points along an equipotential line are of equal potential. Potential difference between any two points along a particular equipotential line is zero. No work is required to oe a charge fro one point to the another on the sae equipotential. An equipotential surface ust be perpendicular to the electric field at any point. (If this is not so E coponents parallel to the surface which would require work to oe the charge along the surface and thus contradict the idea of equipotential). Electric field lines and equipotentials are utually perpendicular. The negatie plate is usually arbitrarily chosen to be zero olts. The electric field E points towards lower alues of V. Physics, 5 th Edition Chapter Seenteen: Electric Potential and Electric Energy
Electron Volt (ev) An electron olt is a unit of energy. One electron olt is defined as the energy change of an electron e as a result of oing through a potential difference of 1V. Page 4 of 1eV 1. 19 J An electron that accelerates through a potential difference of 00V will lose 00eV of potential energy and gain 00eV of kinetic energy. Motion in a constant unifor Electric Field The force on a charged particle oing in a unifor electric field is constant in agnitude and direction, thus producing constant acceleration. This force is in the direction of the electric field if the charge is positie and in the opposite direction is the charge is negatie. so F a qe F The otion of a charged particle in a unifor electric field is siilar to the otion of a particle in a unifor graitational field (as the acceleration is constant) and we can expect siilar types of paths. If the charged particle enters the unifor electric field at right angles the path (or trajectory) will be parabolic. The initial horizontal coponent of elocity reaining constant and the Electric Force at right angles to the particle proiding the force and therefore acceleration a Eq qe Physics, 5 th Edition Chapter Seenteen: Electric Potential and Electric Energy
Electron Gun (Worked Exaple) (This coes directly fro an exaple on pg.185 in FOSP, Parha & Webber) An electron gun accelerates electrons through a potential difference of 1.0 V and ejects the at right angles to a unifor electric field so that they traerse the field for a length of 0.. Gien the ass of an electron, 9.1-1 kg, and the charge of an electron, 1. C, calculate: Page 5 of (a) the kinetic energy supplied to each electron by the electron gun. The electrons are accelerated in the electric field of the gun. The work done on an electron is gien by: qv 1. 1. 17 This is equal to the increase in kinetic energy of the electron. (b) the elocity with which each electron enters the field (assuing that it left the filaent of the gun at zero elocity). Since the initial kinetic energy of the electron was assued to be zero, the final kinetic energy is: (c) 1 1. 5.9-17 1. 9.1-17 J -1 J kg 1 J. 9. 1 the tie taken for an electron to traerse the field. The tie take to traerse the field at unifor horizontal elocity is gien by: l t -1 5.9 1. 7-8 s 1 5. 9 7 14 Physics, 5 th Edition Chapter Seenteen: Electric Potential and Electric Energy
(d) If the electric field strength is.0 olts per etre, what is the acceleration of each electron in the field? The force on the electron is gien by FeE, and thus the acceleration is found fro: (e) a ee 1.. 9.1.5 9.1 15 14 1 What is the electron s final elocity on leaing the field? The upward elocity on leaing the field is: Hence and tan θ θ t at. 0 8.4 at 45 - ( 5. 9 ) + (. 0 ) 0.5. 5. 0 5. 9 The final elocity is 8.4-1 at an angle of 45.5 aboe the horizontal. Actiities 1. Consider Suary (p.51) - oit capacitor and dielectrics. Attept Saple Questions. Questions (p.5: no.1, 5, 7) 4. Proble (p.5,5: no.1,, 4, 5, ) 5. Foratie Tests 14 1-1 1.7-8 Page of Physics, 5 th Edition Chapter Seenteen: Electric Potential and Electric Energy