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.
Transcript
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.
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Generators as Energy Converters
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Motion does not necessarily
mean changing magnetic flux!
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
Finding the direction of the induced current
Induced Electric Fields
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Electric field around a solenoid with alternating current
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Current : I(t) = Imax cos(ωt)
Magnetic field inside the solenoid :
B(t) = μ0nI(t) (outside B = 0)
Flux through the surface bounded by the path :
ΦB (t) = B(t) ⋅πR2
Electric field circulation around the path :
E ⋅ds = E ⋅2πr = −dΦB
dt∫ = μ0nImaxπR
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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!
Magnetospheric and Ionospheric Current SystemsMagnetospheric 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
• 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
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."
Historical EventsHistorical Events
Historical EventsHistorical EventsMarch 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
Eddy Currents
When magnetic field is on, currents (eddy currents) are induced in conductors so that the pendulum slows down or stops
Displacement Current
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