Physics 2102 Lecture: 07 TUE 09 FEBPowerPoint PresentationSlide 3Slide 4Continuous Charge DistributionsPotential of Continuous Charge Distribution: Line of ChargeElectric Field & Potential: A Simple Relationship!E from V: ExampleSlide 9Slide 10Equipotentials and ConductorsConductors Change the Field Around Them!Sharp ConductorsSlide 14LIGHTNING SAFE CROUCHSummary:Slide 17Electric Potential IIElectric Potential IIPhysics 2102Jonathan DowlingPhysics 2102 Physics 2102 Lecture: 07 TUE 09 FEBLecture: 07 TUE 09 FEBQuickTime™ and a decompressorare needed to see this picture.PHYS2102 FIRST MIDTERM EXAM!6–7PM THU 11 FEB 2009Dowling’s Sec. 4 in ???YOU MUST BRING YOUR STUDENT ID!YOU MUST WRITE UNITS TO GET FULL CREDIT!The exam will cover chapters 21 through 24, as covered in homework sets 1, 2, and 3. The formula sheet for the exam can be found here:http://www.phys.lsu.edu/classes/spring2010/phys2102/formulasheet.pdf KNOW SI PREFIXES n, cm, k, etc.Conservative Forces, Work, and Potential Energy€ W = F r( )∫drWork Done (W) is Integral of Force (F)€ U = −WPotential Energy (U) is Negative of Work Done € F r( )= −dUdrHence Force is Negative Derivative of Potential EnergyCoulomb’s Law for Point ChargeP1P2q1q2P1P2q2€ F12=kq1q2r2€ F12= −dU12drForce [N]= Newton€ U12=kq1q2r€ U12= − F12dr∫Potential Energy [J]=JouleElectricPotential [J/C]=[V]=Volt€ V12=kq2r€ V12= − E12dr∫ € v E 12=kq2r2ElectricField [N/C]=[V/m]€ E12= −dV12drContinuous Charge Continuous Charge DistributionsDistributions•Divide the charge distribution into differential elements•Write down an expression for potential from a typical element — treat as point charge•Integrate!•Simple example: circular rod of radius r, total charge Q; find V at center.dqr€ V = dV∫=kdqr∫=krdq∫=krQ€ Units : Nm2C2Cm ⎡ ⎣ ⎢ ⎤ ⎦ ⎥=NmC ⎡ ⎣ ⎢ ⎤ ⎦ ⎥=JC ⎡ ⎣ ⎢ ⎤ ⎦ ⎥≡ V[ ]Potential of Continuous Charge Potential of Continuous Charge Distribution: Line of Charge Distribution: Line of Charge /Q Lλ =dxdq λ=∫∫−+==LxaLdxkrkdqV0)(λ[ ]LxaLk0)ln( −+−= λ⎥⎦⎤⎢⎣⎡+=aaLkV lnλ⎥⎦⎤⎢⎣⎡+=aaLkV lnλ•Uniformly charged rod•Total charge Q•Length L•What is V at position P?PxLadxUnits: [Nm2/C2][C/m]=[Nm/C]=[J/C]=[V]Electric Field & Potential: Electric Field & Potential: A A Simple Relationship!Simple Relationship!Notice the following:•Point charge:E = kQ/r2V = kQ/r•Dipole (far away):E = kp/r3V = kp/r2•E is given by a DERIVATIVE of V!•Of course! dxdVEx−=dxdVEx−=Focus only on a simple case: electric field that points along +x axis but whose magnitude varies with x. Note: • MINUS sign!• Units for E: VOLTS/METER (V/m)Note: • MINUS sign!• Units for E: VOLTS/METER (V/m)fiV E dsΔ =− •∫rrfiV E dsΔ =− •∫rrE from V: Example E from V: Example /Q Lλ =€ V = kλ lnL + aa ⎡ ⎣ ⎢ ⎤ ⎦ ⎥= kλ ln L + a[ ]− ln a[ ]{ }€ V = kλ lnL + aa ⎡ ⎣ ⎢ ⎤ ⎦ ⎥= kλ ln L + a[ ]− ln a[ ]{ }•Uniformly charged rod•Total charge Q•Length L•We Found V at P!•Find E from V?PxLadx€ E = −dVda= −kλddaln L + a[ ]− ln a[ ]{ }= −kλ1L + a−1a ⎧ ⎨ ⎩ ⎫ ⎬ ⎭= −kλa − L + a( )L + a( )a ⎧ ⎨ ⎩ ⎫ ⎬ ⎭= kλLL + a( )a ⎧ ⎨ ⎩ ⎫ ⎬ ⎭€ E = −dVda= −kλddaln L + a[ ]− ln a[ ]{ }= −kλ1L + a−1a ⎧ ⎨ ⎩ ⎫ ⎬ ⎭= −kλa − L + a( )L + a( )a ⎧ ⎨ ⎩ ⎫ ⎬ ⎭= kλLL + a( )a ⎧ ⎨ ⎩ ⎫ ⎬ ⎭Units:€ Nm2C2Cmmm2 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥=NC ⎡ ⎣ ⎢ ⎤ ⎦ ⎥=Vm ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ √ Electric Field!Electric Field & Potential: Electric Field & Potential: Question Question •Hollow metal sphere of radius R has a charge +q•Which of the following is the electric potential V as a function of distance r from center of sphere?+qVr1≈rr=R(a)Vr1≈rr=R(c)Vr1≈rr=R(b)+qOutside the sphere:• Replace by point charge!Inside the sphere:• E =0 (Gauss’ Law) • E = –dV/drM= 0 IFF V=constant2dVEdrd Qkdr rQkr=−⎡ ⎤=−⎢ ⎥⎣ ⎦=2dVEdrd Qkdr rQkr=−⎡ ⎤=−⎢ ⎥⎣ ⎦=Vr1≈Electric Field & Potential: Electric Field & Potential: Example Example E21r≈Equipotentials and Equipotentials and ConductorsConductors•Conducting surfaces are EQUIPOTENTIALs •At surface of conductor, E is normal (perpendicular) to surface•Hence, no work needed to move a charge from one point on a conductor surface to another •Equipotentials are normal to E, so they follow the shape of the conductor near the surface.EVConductors Change the Conductors Change the Field Around Them!Field Around Them!An Uncharged Conductor:A Uniform Electric Field:An Uncharged Conductor in the Initially Uniform Electric Field:Sharp ConductorsSharp Conductors•Charge density is higher at conductor surfaces that have small radius of curvature•E = for a conductor, hence STRONGER electric fields at sharply curved surfaces!•Used for attracting or getting rid of charge: –lightning rods–Van de Graaf -- metal brush transfers charge from rubber belt–Mars pathfinder mission -- tungsten points used to get rid of accumulated charge on rover (electric breakdown on Mars occurs at ~100 V/m)(NASA)Ben Franklin Invents the Lightning Rod!LIGHTNING SAFE CROUCHIf caught out of doors during an approaching storm and your skin tingles or hair tries to stand on end, immediately do the "LIGHTNING SAFE CROUCH ”. Squat low to the ground on the balls of your feet, with your feet close together. Place your hands on your knees, with your head between them. Be the smallest target possible, and minimize your contact with the ground.Summary:Summary:•Electric potential: work needed to bring +1C from infinity; units = V = Volt•Electric potential uniquely defined for every point in space -- independent of path!•Electric potential is a scalar -- add contributions from individual point charges•We calculated the electric potential produced by a single charge: VM=Mkq/r, and by continuous charge distributions : VM=Mkdq/r•Electric field and electric potential: E= -dV/dx•Electric potential energy: work used to build the system, charge by charge. Use W=U=qV for each charge.•Conductors: the charges move to make their surface equipotentials. •Charge density and electric field are higher on sharp points of
View Full Document
Unlocking...