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8/28/00 NE 409. Relativistic Dynamics Electromagnetic Fields What happens if the electric ( E ) and Magnetic ( B ) fields are in a moving reference frame?. Charged particle in an electric and magnetic field in S frame. E. B. S. V. q. Lorentz force in S frame. q = ( E + V x B ) = 0.

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8/28/00 NE 409

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8 28 00 ne 409

8/28/00 NE 409

  • Relativistic Dynamics

    • Electromagnetic Fields

      • What happens if the electric (E) and Magnetic (B) fields are in a moving reference frame?


Charged particle in an electric and magnetic field in s frame

Charged particle in an electric and magnetic field in S frame

E

B

S

V

q


Lorentz force in s frame

Lorentz force in S frame

q = (E + VxB) = 0


Motion in s frame

Motion in S’ frame

  • Suppose that S’ is chosen so that it moves in the direction of the particle motion with a velocity equal to the particle velocity. In the S’ frame the particle appears to be stationary.

  • Here, the VxB term in the Lorentz equation is zero.


Since the force equal zero in both the s and s frame

Since the force equal zero in both the S and S’ frame

  • E = 0 in the S’ frame.

  • Conclusion

    • E and B look different to observers in different frames of reference. E and B are related depending upon the motion of the reference frame. This is why we call E and B electromagnetic fields rather than electric and magnetic fields.


Transformation of electric and magnetic fields from s to s frame of reference

Transformation of electric and magnetic fields from S’ to S frame of reference

  • E’|| = E||

  • E’ ^= g( E ^+U x B^)

  • B’|| = B||

  • B’ ^= g( B ^- U x E^/c2)


Summary

Summary

  • Newtonian mechanics is a specific case of relativistic mechanics (u << c).

  • Special relativity assumes that all inertial frames of reference are equivalent

  • General relativity assumes that all possible reference frames are equivalent.


Mass defect

Mass Defect

  • Radius of atom is about 1 angstrom. This is about 0.1 nanometer.

  • Radius of a nucleus is about 10-5 angstroms. This is about 10-15 meters.

  • Atomic Number = Z, is the number of electrons or protons in an atom.

  • Atomic Mass = A, is the mass in Atomic Mass Units (AMU)


More facts

More facts

  • A is about equal to the number of protons plus the number of neutrons in an atom.

  • Mass of electron = me = 0.511 MeV/c2 or 9.11x10-31 kg.

  • Mass of proton = mp = 938.3 MeV/c2 or 1.673x10-27 kg.

  • Mass of neutron = mn = 939.6 MeV/c2 or 1.675x10-27 kg.


Even more facts

Even More Facts

  • Number of Neutrons = N

  • A = Z + N


Mass deficit for oxygen

Mass Deficit for Oxygen


Differential mass

Differential Mass

The resulting mass change must go into energy according to the mass energy relationship,


Binding energy

Binding Energy

  • This energy is known as the binding energy. In order to break apart the atom into its basic components, you would need to put in an energy equivalent to the binding energy of the atom.

  • Binding Energy per Nucleon = Dmc2/A


Quantum mechanics

Quantum Mechanics

  • The second great development in modern physics is quantum mechanics.

  • Quantum mechanics was developed to describe the behavior of atoms.


Questions

Questions?


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