lect19 - Physics 227: Exam 2 Information • Note: exam 2:...

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Unformatted text preview: Physics 227: Exam 2 Information • Note: exam 2: 16 questions covering chapters 25 - 28 • • • • Thursday, Nov 17, 2011, 9:40 PM - 11:00 PM Room assignments: • A-I Arc 103 • J-M SEC 111 - probably starts 9:50 or 10:00. • N-R PLH • S-Z Beck Auditorium, Livingston Campus!!! (NOT Hill 114) Anyone with a conflict should contact Prof. Cizewski ASAP Bring pencils, 1 formula sheet w/ anything you want, NO calculators or other electronics needed or allowed! Thursday, November 10, 2011 Physics 227: Lecture 19 Comments on Electric Fields, Eddy Currents, Superconductivity • Lecture 18 review: • • • • • Faraday’s Law: ε = - dφB/dt. Lenz’s Law: ε o pposes change. Alternators. Generators. Motional emf. Thursday, November 10, 2011 Today: lots of nice demos! Superconducting iClicker The emf, when the loop shown is pulled out of the magnetic field region, is ε = 0.4x0.02xB V CW. Usually I =V /R. But if the loop is superconducting, what is the current in it? A. ε / R = ε / 0 = ∞ A. B. It cannot be ∞, so it must be 0. The superconductor is not special - there w ill be an emf and non-∞ current, but we do not know how to calculate it. Thursday, November 10, 2011 C. Because it is a superconductor, ε = 0 and I = 0. D. It is some number between 0 and ∞ that we do not know how to calculate. E. It is some number between 0 and ∞ that cannot be calculated in principle - it is random. Maxwell’s Equations In the late 1800s the knowledge of electric and magnetic fields was summarized with Maxwell’s Equations: ρ ￿￿ ∇·E = ￿0 ￿￿ ∇·B =0 ￿ ∂B ￿ ￿ ∇×E =− ∂t ￿ qenclosed ￿ ￿ E · dA = ￿0 ￿ There are no magnetic ￿ ￿ B · dA = 0 Gauss’s Law: electric fields start/stop on charges. charges. ￿ Changing magnetic dφB ￿s fields generate electric E · d￿ = − dt fields. Today! Magnetic fields result ￿ ∂E ￿ × B = µ0 ￿0 ￿ ￿ from currents and ∇ + µ0 J changing electric fields. ∂t ￿ 1 dφE ￿s + µ0 ienc B · d￿ = 2 c dt Thursday, November 10, 2011 EMF And Electric Fields We have now seen that there are two different origins for electric fields, that lead to two different types of fields. We first learned that charge distributions lead to electric fields that start / stop on the charges. These electric fields are derivatives / slopes of voltages, so the line integral of E.dl is the voltage difference. We now also know that changing magnetic fields lead to emfs and electric fields with a different configuration. The resulting electric field does not start or stop on a charge. Instead, like w ith magnetic fields, these electric fields curl around and form a closed loop. Here the line integral of E.dl around a closed loop is -dφB/dt, but can be arbitrary if the loop is not closed. It is not 0, as it would be if charges were generating the electric field. Thursday, November 10, 2011 Faraday’s Law iClicker x x x solenoid x A. 0 V. B. A (dB/dt) V. C. -A (dB/dt) V. D. (A/2) (dB/dt) V. E. -(A/2) (dB/dt) V. Thursday, November 10, 2011 + V - The current in an ideal solenoid of area A in increasing so that the field increases into the page at a rate dB/dt. This induces an emf in a loop around the solenoid. What voltage does the voltmeter hooked up as shown measure? An emf is not a voltage. For the emf around the loop, there is no reason to think it is more positive on one side than the opposite side - the cylinder part of the probelm is rotationally symmetric. Induced Field / Emf Applications Magnetic regions on spinning disk cause electric signal in pickup coil. Regenerative braking in hybrid car charges batteries. Engine rotation powers spark in airplane engine. A large set of applications will be covered next week, under the topic of ``inductance’’. Thursday, November 10, 2011 Eddy Currents Motion of a conductor through a region of varying magnetic fields leads to e ddy currents circulating around within the conductor. Finite resistance heats the conductor up w ith power P = I2R. Thursday, November 10, 2011 Eddy Currents The eddy currents form patterns, as shown here. If the disk is rotating freely, its mechanical energy is converted to heat and it slows up. You can see that the direction of the magnetic force on the currents, IdlxB, is to the right, opposing the rotation of the disk. This effect leads to several applications for e ddy currents. And some nice demos. Thursday, November 10, 2011 Eddy Current Applications Braking of rotational motion. Metal detectors. Heating materials without mechanical contact (induction heating). Thursday, November 10, 2011 Eddy Current Applications Motion of Io through Jupiter’s magnetic field leads to eddy currents. Io has a liquid magma ocean, which can conduct large currents. http:/ /www.nasa.gov/topics/ solarsystem/features/ galileo20110512.html Thursday, November 10, 2011 Magnets Moving Near Conductors Generally, if I have magnets moving near conductors, or conductors moving near magnets, there are eddy currents which can convert mechanical energy into electric currents, which through P=I2R heat the conductor. Let’s see some examples! Why did the can implode? What happens if we put the can in off-center? Which disk slowed up the most? ... the least? Why? Is gravity different in the tube? Why does one ring jump and not the other? Thursday, November 10, 2011 Superconductors Field expelled from body of superconductor. TC depends on external field. Thursday, November 10, 2011 Demo - done a while ago Thursday, November 10, 2011 Applications Magnetic levitation trains SQUIDS: Superconducting QUantum Interference Devices Electromagnets Power transmission Thursday, November 10, 2011 Eddy Current iClicker In what order do the disks race through a magnetic field? Insulator Conductor Conductor w ith holes Conductor w ith slots B. I, Ch, Cs, C. Ignore changes to the moment of inertia. Assume the B field is constant and the same size as the disks. C. C, Ch, Cs, I. We saw this in demo. A. I, Cs, Ch, C. D. C, Cs, Ch, I. E. I, Cs, C, Ch. Thursday, November 10, 2011 Thank you. Prof. Cizewski will be giving the lecture Monday, Nov 14, and a review for the exam on Thursday Nov 17. Thursday, November 10, 2011 ...
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This note was uploaded on 01/03/2012 for the course PHYSICS 750:227 taught by Professor Ronaldgilman during the Fall '11 term at Rutgers.

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