Electrodynamics (I): Homework 5
Due: May 7, 2014
Exercises in Griffiths
12.28, 12.29, 12.31, 12.35, 12.36(10% hand-in), 12.40, 12.41, 12.47, 12.48 (10%, hand-in),
12.60, 12.65(10%, hand-in)
Ex.1 10% hand-in
A perfect conducting sphere of radius R moves with constant velocity v towards +x direction
through a uniform magnetic field B, pointing in +y direction. Suppose v c, find the
surface charge density induced on the sphere to the lowest order in v/c.
Ex.2 hand-in Matter in uniform motion
Consider the transformation of electric field and magnetic field between two inertial frames
~ k and A
~ ⊥ denote components of A
~
that move relative to each other with velocity ~v . Let A
~ and A
~ 0 denote
that are parallel to ~v and perpendicular to V~ respectively. Furthermore, A
the vector field for the same space time point in different inertial frames.
~
(a) 5% Assuming both frames are in vacuum, find transformation rules for the fields D
~
(electric displacement field) and H.
~
(b) 5 % If we assume that results of (a) are also true for materials with magnetization M
~ and P~ .
and electric polarization P~ , find transformation rules for M
~ and M
~ = χm H,
~ are valid in the rest
(c) 5% As we learned, the linear relations, P~ = 0 χe E
~ and P~ . Suppose that the object with M
~ and P~ moves with
frame of objects that possess M
~ and B
~ in this frame. Find the
constant velocity ~v . The electric and magnetic fields are E
~ and P~ to E,
~ B,
~ D,
~ and H.
~
general linear relations that relate M
1