Direct current (dc) generators

Split ring (commutator) does the job of reversing polarity every half cycle

Motional emf – conductor moving in a constant magnetic field

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FB = qvB will move charges

until compensated by the electric

field of end accumulations

qvB = qE = qV / l

V = Bvl

B Blx

dxBl Blvdt

2 2resistor

/

( ) /

I Blv R

P I R Blv R

Generators as Energy Converters

2

Who does the work?

We! - By moving the bar:

( ) /

Energy conserved

appliedP Fv IBlv Blv R Generator does not produce electric energyout 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 toelectric energy (current)

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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

2ω sin(ωt)

Outside : E(r, t) =μ0nImaxR

2ω

2rsin(ωt)

Inside (R→ r) : E(r, t) =μ0nImaxrω

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