Hints for Assignment 22
10.36
Note that the ordinary acceleration is 
,
where 
is the ordinary velocity.
Partial answers:
(b)
(d) 
10.37 This one can be done with the connection between K and F, or you can do it using the results of 10.36.
10.39
Both the field and the plates get transformed.
Use Lorentz and Pythagoras to handle the plate angle
and unit vectors to find the angle between the
plates and 
.
Partial answer: the field is not perpendicular to
the plates in S.
10.40
(a) Do the surface integral of Eq. 10.103 over a sphere
using spherical coordinates.
(b) When he says find 
he means finds 
,
valid for all points in space using spherical coordinates.
10.47
This is an exercise in playing with tensor multiplication
using index notation.
Use the fact that 
is symmetric and start with
10.50
You will find that F changes but G stays the same.
If the new tensor is called 
, then
you are to build it so that it
involves only D and H and satisfies
10.53 When he says ``work out'' he means find out what it means in terms of ordinary force and particle velocity. The answer involves a familiar idea involving power which you first encountered in Physics 121. It will be helpful to look at Eq. (83).