Electrodynamics (I): Homework 4
Due: April 16, 2015
Exercises in Griffiths
12.2, 12.6, 12.16, 12.19, 12.59 (hand-in 5%)
Ex.1 5% hand-in
An observer O at rest with respect to fixed distant starts observes an isotropic distribution
of stars, dN =
N
dΩ,
4π
in any solid angle dΩ. Here N is the total number of stars that O
can see. Another observer O0 moves along z-axis relative to O with a large velocity v. Let
θ0 and φ0 be the polar (with respect to z-axis) and azimuthal angles in the inertial frame
of O0 . P 0 (θ0 , φ0 )dΩ0 is the number of stars in the solid angle dΩ0 = sin θ0 dθ0 dφ0 seen by
O0 . Assuming that every star seen by O can be seen by O0 and vice versa, find P 0 (θ0 , φ0 ).
Discuss the limit v → c for θ0 = 0 and θ0 = π.
Ex.2 5% hand-in
As shown in the following figure, a mirror moves with velocity v towards −x̂ direction. A
light is incident from right with α being the incident angle and β being the reflection angle.
Express cos β in terms of cos α and v.
1