Transcript Electric Potential - McMaster Physics & Astronomy Outreach

Loose ends and
Magnetic Fields in Astronomy
- Exam tips – come to class!
- Course Evaluations – come to class!
- 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
c 1
• Since B = E/c and
uB  uE 
1
2
εo E 
2
B
2
2 μo
μ oεo
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 εoE2max = 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 distance
r from the nucleus of an atom. Combining these, we can
show that:
 e 
This is the magnetic moment of an
 
L

electron
 2m 
Where does magnetism come from ????
Now, because the angular momentum L for electrons is
quantized, L= 0 ,  , 2  ,3  ....
The smallest possible non-zero value of the magnetic
moment is :
 e 
 

 2m 
Q: So, if all electrons have this unit of magnetic moment,
why are not all substances magnetic ???
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 Galaxy
Distribution
Computer simulations of large scale structure formation
HDF and early
galaxy formation