1. Chapters E12 (and E13) The Electromagnetic Field

2. The Sun’s magnetism The atmosphere of the sun is a conducting plasma, electric currents cause magnetic fields that in turn affect the currents. We are only beginning to understand how this very complex system works

3. Solar flares can release the energy equivalent of billions of atomic bombs in the span of just a few minutes. These explosions give off a burst of x- rays and charged particles, some of which may later hit Earth, endangering satellites and causing power outages. Scientific American, April 2006

4. Magnetism of the sun The sun’s tumultuous magnetic fields provide the fuel of flares. The sudden release of energy in a flare results from a process called reconnection, whereby oppositely directed magnetic field lines come together and partially annihilate each other. Although theoretical studies of magnetic reconnection on the sun have been carried out for decades, only recently have space probes uncovered observational evidence for this phenomenon. The telltale signs include pointed magnetic loops located below the spot where magnetic reconnection is taking place.

5. October 2003 auroral display in Alaska due to a sun flare.

6. POST-FLARE LOOPS sometimes show a distinct cusp at the top. This geometry of the glowing gas reflects a pinching of the local magnetic field. Such pinching can bring about the magnetic reconnection needed to power flares and sometimes remains in evidence for days afterward.

7. The energy source for solar flares is a phenomenon called magnetic reconnection, in which the sun’s magnetic field lines join and quickly reconfigure themselves. Such reconnection events draw energy from the magnetic field, using it to heat the sun’s atmosphere locally and to accelerate charged particles to high speeds.

8. A limiting factor on whether or not man will be able to spend time in space are cosmic rays, charged particles moving close to the speed of light. One way to counteract this is to have a magnetic field to deflect the particles. (Scientific American, March 2006)

9. A return to the theory of relativity The theory of relativity requires that the laws of physics be the same in all inertial reference frames. The equations we have for E and B are: Note: That in a coordinate system in which the charge is at rest, (v=0), there is no magnetic field. Yet in all coordinate systems the particle must feel a force. We must find a way to explain the force in the system where the particle is at rest.

10. According to the theory of relativity, if a particle feels a force in one system (is accelerated) the same force must exist in all inertial systems. However, it is not necessary that the force be due to the same cause. In our situation, if the particle is moving it feels a magnetic force. If it is standing still what causes the force?

11. Case 1. The reference frame is one in which the electron is moving with constant velocity and the current carrying (but neutral) wire is at rest but has electrons moving with the same velocity as the one outside the wire. E=0 v - What is the direction of the magnetic force on this electron? v +-+- +-+- +-+- +-+- +-+- +-+- +-+- +-+- Only the electrons in the wire are moving, the protons (wire itself) are at rest.

12. Case 2. The reference frame is one in which all the electrons are at rest and the wire (protons) moving with constant velocity. - v+-+- +-+- +-+- +-+- +-+- +-+- + +-+- +++++ Because they are moving, the protons have less distance between them: The result is a net positive charge and an electric force on the electron in the direction of the wire. In this case the force that accelerates the electron toward the wire is electrical.

13. Chapter E13 Maxwell’s Equations Changing Electric and Magnetic Fields

14. You need to be able to write a paragraph explaining what each of the following means. The total electrical flux through a closed surface is determined by the charge enclosed by the surface. The total magnetic circulation around a closed loop is determined by the current through that area enclosed by the loop plus the rate at which the electric flux through that area is changing in time.

15. You need to be able to write a paragraph explaining what each of the following means. The total magnetic flux through a closed surface always zero. The total electric circulation around a closed loop is determined by the rate at which the magnetic flux through the area enclosed is changing in time.

16. In summary If the magnetic field in a region of space is changing, this causes an electric field. If the electrical field in a region of space is changing in time, this causes a magnetic field.