16.1
(a)
Because the electron has a negative charge, it experiences a force in the direction opposite
to the field and, when released from rest, will move in the negative x-direction. The work
done on the electron by the field is
(b)
The change in the electric potential energy is the negative of the work done on the particle
by the field. Thus,
(c)
Since the Coulomb force is a conservative force, conservation of energy gives
, or
, and
16.5
16.6
(a)
(b)
(c)
(d)
16.8
(a)
Using conservation of energy,
“stopped,” we have
The required stopping potential is then
, with
since the particle is
(b)
Being more massive than electrons, protons traveling at the same initial speed will have
more initial kinetic energy and
(c)
Since
, the ratio of the stopping potential for a
proton to that for an electron having the same initial speed is
16.12
(a)
(b)
16.13
16.14
(a)
Calling the
(b)
Replacing
charge
,
in part (a) yields
, and
since the final location of the
is an infinite distance
from other charges. The potential, due to the other charges, at the initial location of the
. Thus, the required energy for the move is
is