1. 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

2. Energy Density in EM Waves The energy density, u, is the energy per unit volume For the electric field, u E = ½ ε o E 2 For the magnetic field, u B = ½ μ o B 2 Since B = E/c and

3. 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

4. Energy Density The total instantaneous energy density is the sum of the energy densities associated with each field –u =u E + u B = ε o E 2 = B 2 / μ o When this is averaged over one or more cycles, the total average becomes –u av = ε o (E 2 ) av = ½ ε o E 2 max = B 2 max / 2μ o

5. Where does magnetism come from ???? Recall these equations: I=Q/t T=2πr/v L=mvr μ=IA (sub in the above, and A=πr 2 ) Imagine a little circuit with an electron moving at a distance r from the nucleus of an atom. Combining these, we can show that: This is the magnetic moment of an electron

6. Where does magnetism come from ???? Now, because the angular momentum L for electrons is quantized, L= The smallest possible non-zero value of the magnetic moment is : Q: So, if all electrons have this unit of magnetic moment, why are not all substances magnetic ???

7. EM in Astronomy

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

9. This is the spiral galaxy M51 and its magnetic field. Studying the fields helps us understand how galaxies form and evolve.

10. This is the jet of M87, evidence for a super massive black hole at the center of this galaxy.

11. Sunspots are caused by strong magnetic fields on the surface of the sun. We can detect them on other stars currently!

12. A supercomputer simulation of the reversal of earth’s magnetic field The earth’s magnetic field.

13. Planetary formation needs to incorporate magnetic fields in the ‘protoplanetary’ disc. These are called MHD (magneto-hydro-dynamics simulations.

14. Redshift of EM waves

15. Galaxy distribution

17. Large Scale Galaxy Distribution

18. Computer simulations of large scale structure formation

19. HDF and early galaxy formation