Exercise3.2
- 1.
- For the scalar field
, find the followings:
- (1)
-
- (2)
- the value
of
at P.
- 2.
- Find the directional derivative in the direction of
of
at P.
- 3.
- Let
C
. Then show that the vector field
has the scalar potential
and find the potential energy at each point in space.
- 4.
- Suppose the force field
has the potential . Prove that the following equation holds when a mass point with mass moves in this force field and moves from point A to point B.
HereC
are magnitude of the velocity vectors at , respectivelyD
- 5.
- For any scalar fields
, show the followings.
- 6.
- Let the distance of P, Q
be . Then prove the following for the differential operator