PHYS 1444 – Section 02 Lecture #7Potential due to Point ChargesPotential due to Electric DipolesE Determined from VElectrostatic Potential EnergyElectrostatic Potential Energy; Two chargesElectrostatic Potential Energy; Three ChargesElectrostatic Potential Energy: electron VoltCapacitors (or Condensers)CapacitorsSlide 11Determination of CapacitanceExample 24 – 1Slide 14Example 24 – 3Tuesday, Feb. 15, 2011 1PHYS 1444-02 Dr. Andrew BrandtPHYS 1444 – Section 02Lecture #7•Chapter 23:•Chapter 24 Tuesday Feb 15, 2011Dr. Andrew Brandt•Potential from System of Charges•Capacitors and Capacitance•HW3 due Weds at 9pmTuesday, Feb. 15, 2011 2PHYS 1444-02 Dr. Andrew BrandtPotential due to Point Charges•E field due to a point charge Q at a distance r? •Electric potential due to the field E for moving from point ra to rb away from the charge Q isb aV V- =barrE dl- � =�rrE =2014Qrpe=2Qkr20ˆˆ4barrQ rrdrrpe- � =�2014barrQdrrpe=- =�01 14b aQr rpe� �-� �� �3 Potential due to Electric Dipoles r=lcosV =V =014iiaQrpe=�( )014QQr r rpe� �-+ =� �� �+D� �01 14Qr r rpe� �- =� �+D� �04 ( )Q rr r rpeD+D20cos4Q lrqpe=201 cos4pVrqpe=V due to dipole a distance r from the dipoleTuesday, Feb. 15, 2011 PHYS 1444-02 Dr. Andrew BrandtTuesday, Feb. 15, 2011 4PHYS 1444-02 Dr. Andrew BrandtE Determined from V•Potential difference between two points is•So we can write–What are dV and El?•dV is the infinitesimal potential difference between two points separated by the distance dl •El is the field component along the direction of dl.b aV V- =baE dl- ��rrldVEdl=-E =rV- � =ri j k Vx y z� �� � �- + +� �� � �� �rr rTuesday, Feb. 15, 2011 5PHYS 1444-02 Dr. Andrew BrandtElectrostatic Potential Energy•Consider a point charge q that is moved between points a and b where the electrostatic potentials due to other charges are Va and Vb•The change in electrostatic potential energy of q is•Now what is the electrostatic potential energy of a configuration of charges?–Let’s choose V=0 at r=–If there are no other charges around, a single point charge Q1 in isolation has no potential energy and feels no electric forceUD =b aU U- =( )b aq V V- =baqVTuesday, Feb. 15, 2011 6PHYS 1444-02 Dr. Andrew BrandtElectrostatic Potential Energy; Two charges•If a second point charge Q2 is brought close to Q1 at the distance r12, the potential due to Q1 at the position of Q2 is•The potential energy of the two charges relative to V=0 at r= is–This is the work that needs to be done by an external force to bring Q2 from infinity to a distance r12 from Q1.–It is also a negative of the work needed to separate them to infinity.V =10 1214Qrpe2U Q V=1 20 1214Q Qrpe=Tuesday, Feb. 15, 2011 7PHYS 1444-02 Dr. Andrew BrandtElectrostatic Potential Energy; Three Charges•So what do we do for three charges? •Work is needed to bring all three charges together–Work needed to bring Q1 to a certain place without the presence of any charge is 0.–Work needed to bring Q2 to a distance to Q1 is–Work need to bring Q3 to a distance to Q1 and Q2 is•So the total electrostatic potential of the three charge system is12U =3U =U =1 20 1214Q Qrpe13U +1 30 1314Q Qrpe+2 30 2314Q Qrpe23U =12 13 23U U U+ + =[ ]1 3 2 31 20 12 13 231 0 at 4Q Q Q QQ QV rr r rpe� �+ + = =�� �� �Tuesday, Feb. 15, 2011 8PHYS 1444-02 Dr. Andrew BrandtElectrostatic Potential Energy: electron Volt•What is the unit of electrostatic potential energy?–Joules•Joules is a very large unit in dealing with electrons, atoms or molecules•For convenience a new unit, electron volt (eV), is defined–1 eV is defined as the energy acquired by a particle carrying the charge equal to that of an electron (q=e) when it moves across a potential difference of 1V.–How many Joules is 1 eV then?•eV however is not a standard SI unit. You must convert the energy to Joules for computations.1eV =191.6 10 1C V-� � =191.6 10 J-�Tuesday, Feb. 15, 2011 9PHYS 1444-02 Dr. Andrew BrandtCapacitors (or Condensers)•What is a capacitor?–A device that can store electric charge without letting the charge flow•What does it consist of?–Usually consists of two oppositely charged conducting objects (plates or sheets) placed near each other without touching–Why can’t they touch each other?•The charges will neutralize each other•Can you give some examples?–Camera flash, surge protectors, computer keyboard, binary circuits…•How is a capacitor different than a battery?–Battery provides potential difference by storing energy (usually chemical energy) while the capacitor stores charge but very little energy.10Capacitors•A simple capacitor consists of a pair of parallel plates of area A separated by a distance d.–A cylindrical capacitors are essentially parallel plates wrapped around as a cylinder.•How would you draw symbols for a capacitor and a battery?–Capacitor -||-–Battery (+) -|i- (-)Circuit DiagramTuesday, Feb. 15, 2011Tuesday, Feb. 15, 2011 11PHYS 1444-02 Dr. Andrew Brandt•What do you think will happen if a battery is connected (voltage is applied) to a capacitor?–The capacitor gets charged quickly, one plate positive and the other negative with an equal amount. of charge•Each battery terminal, the wires and the plates are conductors. What does this mean?–All conductors are at the same potential. –the full battery voltage is applied across the capacitor plates.•So for a given capacitor, the amount of charge stored in the capacitor is proportional to the potential difference Vba between the plates. How would you write this formula?–C is a proportionality constant, called capacitance of the device.–What is the unit? CapacitorsbaQ CV=C/V or Farad (F)C is a property of a capacitor so does not depend on Q or V.Normally use F or pF.Tuesday, Feb. 15, 2011 12PHYS 1444-02 Dr. Andrew BrandtDetermination of Capacitance•C can be determined analytically for capacitors w/ simple geometry and air in between.•Let’s consider a parallel plate capacitor.–Plates have area A each and separated by d.•d is smaller than the length, so E is uniform.–For parallel plates E=0, where is the surface charge density.•E and V are related•Since we take the integral from the lower potential point a to the higher potential point b along the field line, we obtain• •So from the
View Full Document
Unlocking...