PHYS 1444 – Section 004 Lecture #5AnnouncementsElectric PotentialSlide 4A Few Things about Electric PotentialExample 23 – 1Electric Potential and Potential EnergyComparisons of Potential EnergiesSlide 9Some Typical VoltagesExample 23 – 2Slide 12Electric Potential and Electric FieldMonday, Feb. 5, 2007 1 PHYS 1444-004, Spring 2007Dr. Andrew BrandtPHYS 1444 – Section 004Lecture #5Monday, Feb. 5, 2007Dr. Andrew Brandt•Electric Potential•Electric Potential and Electric FieldMonday, Feb. 5, 2007 2 PHYS 1444-004, Spring 2007Dr. Andrew BrandtAnnouncements•HW1 performance was not good (avg. <70)•HW2 is due Weds 2/7•HW3 is due Thurs 2/15 (posted earlier and due later so it need not wreck your Valentine’s DayMonday, Feb. 5, 2007 3 PHYS 1444-501, Spring 2007Dr. Andrew BrandtElectric Potential•How is the electric field defined?–Electric force per unit charge: F/q•We can define electric potential (potential) as –The electric potential energy per unit charge–This is like the voltage of a battery…•Electric potential is written with a symbol V–If a positive test charge q has potential energy Ua at a point a, the electric potential of the charge at that point isaaUVq=Monday, Feb. 5, 2007 4 PHYS 1444-501, Spring 2007Dr. Andrew BrandtElectric Potential•Since only the difference in potential energy is meaningful, only the potential difference between two points is measurable•What happens when the electric force does “positive work”?–The charge gains kinetic energy–Electric potential energy of the charge decreases•Thus the difference in potential energy is the same as the negative of the work, Wba, done on the charge by the electric field to move the charge from point a to b.•The potential difference Vba isbaV =b aV V- =b aU Uq-=baWq-Monday, Feb. 5, 2007 5 PHYS 1444-501, Spring 2007Dr. Andrew Brandt•What does the electric potential depend on?–Other charges that creates the field–What about the test charge?•No, the electric potential is independent of the test charge•Test charge gains potential energy by existing in the potential created by other charges•Which plate is at a higher potential?–Positive plate. Why?•Since positive charge has the greatest potential energy on it.–What happens to the positive charge if it is let go?•It moves from higher potential to lower potential–How about a negative charge?•Its potential energy is higher on the negative plate. Thus, it moves from negative plate to positive. Potential difference is the same for a negative charge at the negative plate as a positive charge at the positive plate.•The unit of the electric potential is Volt (V).•From the definition, 1V = 1J/C.Zero point of electric potential can be chosen arbitrarily.Often the ground, a conductor connected to Earth is zero.A Few Things about Electric PotentialMonday, Feb. 5, 2007 6 PHYS 1444-501, Spring 2007Dr. Andrew BrandtExample 23 – 1 A negative charge: Suppose a negative charge, such as an electron, is placed at point b in the figure. If the electron is free to move, will its electric potential energy increase or decrease? How will the electric potential change?•An electron placed at point b will move toward the positive plate since it was released at its highest potential energy point.•It will gain kinetic energy as it moves toward left, decreasing its potential energy.•The electron, however, moves from the point b at a lower potential to point a at a higher potential. V=Va-Vb>0.•This is because the potential is generated by the charges on the plates not by the electron.Monday, Feb. 5, 2007 7 PHYS 1444-004, Spring 2007Dr. Andrew BrandtElectric Potential and Potential Energy •What is the definition of the electric potential?–The potential energy difference per unit charge•How would you express the potential energy that a charge q would obtain when it is moved between point a and b with the potential difference Vba?–In other words, if an object with charge q moves through a potential difference Vba, its potential energy changes by qVba.•So electric potential is–A measure of how much energy an electric charge can acquire in a given situation–related to how much work a given charge can do.b aU U- =( )b aq V V- =baqVMonday, Feb. 5, 2007 8 PHYS 1444-004, Spring 2007Dr. Andrew BrandtComparisons of Potential Energies •Let’s compare gravitational and electric potential energies2mm•What are the potential energies of the rocks?–mgh and 2mgh•Which rock has a bigger potential energy?–The rock with a larger mass•Why?–It’s got a bigger mass.•What are the potential energies of the charges?–+QVba and +2QVba •Which object has a bigger potential energy?–The object with a larger charge.•Why?–It’s got a bigger charge.The “potential” is the same but the heavier rock or larger charge can do a greater work.Monday, Feb. 5, 2007 9 PHYS 1444-004, Spring 2007Dr. Andrew BrandtElectric Potential and Potential Energy •The electric potential difference gives potential energy (or the possibility to do work) based on the charge of the object.•So what is happening in batteries or generators?–They maintain a potential difference.–The actual amount of energy used or transformed depends on how much charge flows.–How much is the potential difference maintained by a car’s battery?•12Volts–If for a given period, 5C charge flows through the headlight lamp, what is the total energy transformed?•Etot=5C*12V=60 What is the unit? –If it is left on twice as long? Etot=10C*12V=120J.C*J/C=J (Joules)Monday, Feb. 5, 2007 10 PHYS 1444-004, Spring 2007Dr. Andrew BrandtSome Typical Voltages Sources Approximate Voltage Thundercloud to ground 108 VHigh-Voltage Power Lines 106 VPower supply for TV tube 104 VAutomobile ignition 104 VHousehold outlet 102 VAutomobile battery 12 VFlashlight battery 1.5 VResting potential across nerve membrane 10-1 VPotential changes on skin (EKG and EEG) 10-4 VMonday, Feb. 5, 2007 11 PHYS 1444-004, Spring 2007Dr. Andrew BrandtExample 23 – 2 Electrons in a TV tube: Suppose an electron in the picture tube of a television set is accelerated from rest through a potential difference Vba=+5000V. (a) What is the change in potential energy of the electron? (b) What is the speed of the electron (m=9.1x10-31kg) as a result of this acceleration? (c) Repeat for a proton (m=1.67x10-27kg) that accelerates through a potential difference of Vba=-5000V. •(a)
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