1 Phys 571 , Fall 2010
FINAL EXAM Solutions 1. (a) Fields outside the cylinder are (frame K ) E= and inside E= where a is the cylinder radius. Frame K must move along the z -axes. Indeed, in that case E = B = 0 in both frames. Now 1 E = (E + V B ) , c Fro
1 Phys 571 , Fall 2010
Assignment #5 Due: Nov 3rd, 2010 1. Prove Greens reciprocation theorem: If is the potential due to a volume-charge density within volume V and a surface-charge density on the conducting surface S bounding the volume V , while is the
1 Phys 571 , Fall 2010
Solution to Assignment #4. 1. The dierence between the two gauges is A A= Since 2. 3. (a) E = (E V B /c) ( 1)V VE V2 VB V2 ( f ) = 0, magnetic eld is the same. xyB 2
B = (B + V E /c) ( 1)V
(b) There are innitely many solutions to th
1 Phys 571 , Fall 2010
Assignment #4 Due:9/29/10 1. Prove that for a constant magnetic eld B the following two gauges are equivalent, i.e. lead
1 to the same eld: A = By x and A = 2 B r. Find the gauge transformation that connects
A and A . 2. Given the 4
1 Phys 571 , Fall 2010
Solution to Assignment #3. 1. In the proper frame element of the solid angle is d0 = 2 sin 0 d0 . Therefore, the fraction of photons moving inside d0 is dN = Now, we derived before that cos 0 = Substituting we get d0 = Thus, in the
1 Phys 571 , Fall 2010
Assignment #3 Due: 9/22/2010 1. 0 -meson moving with velocity v decays into two photons (massless quanta of EM eld). In the proper frame of 0 distribution of photons is spherically symmetric. Find the distribution of photons in the
1 Phys 571 , Fall 2010
Assignment #2 Due: 9/8/2010 1. Express the components of 4-acceleration w as a function of the velocity v and acceleration
2 w. Find w in terms of w and w v . Useful identity: (w v )2 = w2 v 2 (w v )2 .
2. A bundle of light rays for
1 Phys 571 , Fall 2010
Solution to assignment # 1 1. Applying two successive boosts K K K : x = (x vt), t = (t vx/c2 ); and x = (x v t ), t = (t v x /c2 ) we have x = [ (x vt) v (t vx/c2 )] = [x(1 + v v /c2 ) t(v + v )] On the other hand, the direct boost
1 Phys 571 , Fall 2010
Assignment #1 Due: 8/30/2010 1. Show explicitly that two successive Lorentz transformations in the same direction are equivalent to a single Lorentz transformation with a velocity v= v1 + v2 . 1 + (v1 v2 /c2 )
2. Two rods of proper
1 Phys 571 , Fall 2010
Assignment #6 Due: Nov 10th, 2010 1. Using the method of images, discuss the problem of a point charge q inside a hollow, grounded, conducting sphere of inner radius a. Find (a) the potential inside the sphere; (b) the induced surfa