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
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