The final will be Thursday, May 7 @ 8:00 AM. It will be 40% comprehensive and 60% what we have covered since the last exam. It will be open book/note.

We will have two review sessions next week:

One on Tuesday at the regular class time

One on Wednesday at at time to be determined (the regular class time?)

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

2ω sin(ωt)

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2ω

2rsin(ωt)

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2sin(ωt)

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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!

Electric currents in Earth's atmosphere can induce currents the planet's crust and oceans. During space weather disturbances, currents associated with the aurora as large as a million-amperes flow through the ionosphere at high latitudes. These currents are not steady but are fluctuating constantly in space and time - produce fluctuating magnetic fields that are felt at the Earth's surface - cause currents called GICs (ground induced currents) to flow in large-scale conductors, both natural (like the rocks in Earth's crust or salty ocean water) and man-made structures (like pipelines, transoceanic cables, and power lines).

Some rocks carry current better than others. Igneous rocks do not conduct electricity very well so the currents tend to take the path of least resistance and flow through man-made conductors that are present on the surface (like pipelines or cables). Regions of North America have significant amounts of igneous rock and thus are particularly susceptible to the effects of GICs on man-made systems. Currents flowing in the ocean contribute to GICs by entering along coastlines. GICs can enter the complex grid of transmission lines that deliver power through their grounding points. The GICs are DC flows. Under extreme space weather conditions, these GICs can cause serious problems for the operation of the power distribution networks by disrupting the operation of transformers that step voltages up and down throughout the network.

Space Weather Causes Currents in Electric Power Grids

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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The Reality of Displacement Current

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