Motional emf – conductor moving in a constant magnetic field

1. There will be one last homework assigned today. It will not be due until the day of the final, Dec 13. I will also put some practice problems on line today. There will be a problem solving session tomorrow, Nov 30. I will not be here next week. The last lecture will be given by another professor. However, you may email with questions. The final is Dec 13 at 2 PM. Remember that it will be 40% comprehensive and 60% on material covered since the last exam. You will be allowed two 8 ½ X 11 sheets of paper for notes (both sides) and it is open book. I will have a review session the day before the final. Look at your schedule and think about when you would like to have it. I am available all day. We will discuss this on Thursday.

2. Motional emf – conductor moving in a constant magnetic field

3. Generators as Energy Converters Generator does not produce electric energy out of nowhere – it is supplied by whatever entity that keeps the rod moving. All it does is to convert it to a different form, namely to electric energy (current)

4. Motion does not necessarily mean changing magnetic flux!

5. Significance of the minus sign – Lenz’s Law Induced current has such direction that its own flux opposes the change of the external magnetic flux Magnetic field of the induced current wants to decrease the total flux Magnetic field of the induced current wants to increase the total flux Correspondingly, magnetic forces oppose the motion – consistently with conservation of energy! Lenz’s Law – the direction of any magnetic induction effect as to oppose the cause of the effect Lenz’s Law – a direct consequence of the energy conservation principle

6. Finding the direction of the induced current

7. Induced Electric Fields

8. Electric field around a solenoid with alternating current

10. We cannot change magnitude of the velocity of a charged particle in a static magnetic field B BUT We can do it in a time-varying magnetic field B(t) – the resulting electric field E(t) will do the job And that’s indeed how particles are accelerated in betatrons!

11. Magnetospheric and Ionospheric Current Systems Several current systems exist in the magnetosphere: magnetopause current, neutral sheet current, ring current, etc… • These currents close partially within the magnetosphere and partially through ionospheric currents via field-aligned currents or Birkeland currents • magnetic field lines act like current carrying wires • During geomagnetic storms, can be very intense • cause ground induced currents

12. Geomagnetically Induced Currents (GICs) • Ionospheric currents • flow at ~100 km • experience large spatiotemporal variations reflected in variations of the Earth's geomagnetic field • as consequence of Faraday's law of induction, an electric field at the surface of the Earth is induced • surface electric field causes electrical currents, known as geomagnetically induced currents (GIC), to flow in any conducting structure, for example, a power or pipeline grid grounded in the Earth Conducting networks include electrical power transmission grids, oil and gas pipelines, undersea communication cables, telephone and telegraph networks and railways. Can cause problems, such as increased corrosion of pipeline steel and damaged high-voltage power transformers

13. Historical Events • Known since the mid-1800s: • electrical telegraph systems could sometimes run without power during geomagnetic storms, described at the time as operating on the "celestial battery” • other times completely inoperative. • The Great Storm of 1859 • great Auroras of August 28 and September 4 lit up the skies of nearly every major city on the planet. • Communication between two telegraph operators: • - Boston operator (to Portland operator): "Please cut off your battery [power source] entirely for fifteen minutes." • - Portland operator: "Will do so. It is now disconnected." • - Boston: "Mine is disconnected, and we are working with the auroral current. How do you receive my writing?" • - Portland: "Better than with our batteries on. - Current comes and goes gradually."

14. Historical Events • March 24, 1940 • First reported effects on power systems, with voltage dips, large swings in reactive power, and tripping of transformer banks, reported from power companies in the US and Canada • Effects also observed on the telephone and telegraph systems in US • March13, 1989 • severe geomagnetic storm • aurora seen as far south as Florida and Cuba • caused the collapse of the Hydro-Québec power grid in a matter of seconds as equipment protection relays tripped in a cascading sequence of events. • six million people left without power for nine hours • eventual cost – $2 billion • Gas pipelines • currents cause the normal corrosion of pipelines to be accelerated • modern pipelines protected from long-term current flows by a weak counter current of a few amperes - applied so that the pipeline has a net, negative potential relative to ground. • - auroral currents change polarity in minutes, rendering this 'cathodic protection' useless

15. Eddy Currents When magnetic field is on, currents (eddy currents) are induced in conductors so that the pendulum slows down or stops

17. Displacement Current

18. “displacement current” of the electric field flux as opposed to conduction current

19. The Reality of Displacement Current Field in the region outside of the capacitor exists as if the wire were continuous within the capacitor