Loose ends and Loose ends and Magnetic Fields in AstronomyMagnetic Fields in Astronomy

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- energy in fields- magnetism in matter- astronomical applications

Energy Density in EM Waves

• The energy density, u, is the energy per unit volume

• For the electric field, uE= ½ εoE2

• For the magnetic field, uB = ½ μoB2

• Since B = E/c and 1 o oc μ ε

221

2 2B E oo

Bu u ε E

μ

Energy Density

• The instantaneous energy density associated with the magnetic field of an EM wave equals the instantaneous energy density associated with the electric field

– In a given volume, the energy is shared equally by the two fields

Energy Density

• The total instantaneous energy density is the sum of the energy densities associated with each field– u =uE + uB = εoE2 = B2 / μo

• When this is averaged over one or more cycles, the total average becomes – uav = εo(E2)av = ½ εoE2

max = B2max / 2μo

Where does magnetism come from ????

Recall these equations:

I=Q/t

T=2πr/v

L=mvr

μ=IA (sub in the above, and A=πr2)

Imagine a little circuit with an electron moving at a distancer from the nucleus of an atom. Combining these, we can show that: L

m

e

2 This is the magnetic moment of an

electron

Where does magnetism come from ????

Now, because the angular momentum L for electrons isquantized, L=

The smallest possible non-zero value of the magnetic moment is :

m

e

2

Q: So, if all electrons have this unit of magnetic moment, why are not all substances magnetic ???

....3,2,,0

EM in Astronomy

Magnetic fields ‘rotate’ an electromagnetic wave. This is called Faraday Rotation, and it allows us to measure the magnetic field of interstellar space.

This is the spiral

galaxy M51 and its

magnetic field.

Studying the fields

helps us understand

how galaxies form and

evolve.

This is the jet of M87,

evidence for a super

massive black hole at

the center of this

galaxy.

Sunspots are caused by

strong magnetic fields on

the surface of the sun.

We can detect them on other

stars currently!

A supercomputer

simulation of the

reversal of earth’s

magnetic field

The earth’s magnetic field.

Planetary formation needs to incorporate magnetic fields in the ‘protoplanetary’ disc.

These are called MHD (magneto-hydro-dynamics simulations.

Redshift of EM waves

Galaxy distribution

Large Scale GalaxyDistribution

Computer simulations of large scale structure formation

HDF and earlygalaxy formation