Physics 200C Mid Term Exam 04-May-05

Dr. Cebra Name: _________________

Instructions: Work all parts of each problems (each problem worth 50 points). No notes, calculators, etc. Please write your name on every page – they WILL be separated. Staple additional sheet to their respective problems.

1. A neutral pion (p⁰ meson) of rest mass M decays into two photons (g). The angular distribution of these g-rays is isotropic in the rest frame of the p⁰. In the laboratory frame, the p⁰ travels with velocity v in the z direction and decays in flight. (For latter parts of the problem, q is measured in the lab with respect to the z axis.)
1. What is the energy of each g-ray in the rest frame of the p⁰?
2. What is the energy of the g-rays as a function of q in the lab frame?
3. What is the probability P(q)dW that a photon is emitted into solid angle dW about q in the lab frame?
   

Phys 200C Name: _________________

2. A particle with charge Q and mass M accelerates from rest through a constant and uniform electric field E. (Do not assume v/c to be small.)

a. Find the particle’s velocity as a function of time.

b. If the particle decays with the mean life time of t in its rest frame, what is the probability that the particle will survive a distance L from its starting point?

Phys 200C Name: _________________

3. By Lorentz transforming the electric and magnetic fields of a point at rest, one can determine the electric and magnetic fields of a moving point charge (charge Q, mass M).
1. Determine the E and B fields of a point charge moving with velocity v.
2. From these E and B fields from part a., one can determine the electromagnetic energy 4-Tensor T^m_n, where:

The time-like component of represents the rate of energy transferred from the E&M fields. Determine the Poynting vector and show that the total power radiated is zero.