Introductory Physics Volume Two

2.7 More Examples 49
⊲ Problem 2.15
An electron is released from a distance of 2.0 cm from a proton. How
fast will the electron be going when it is 0.5 cm from the proton?
(Assume that the proton does not move.)
§ 2.7 More Examples
Example
An electric field is given by E ⃗ = (3
C·m
)x 2 î). What is the electric
2
potential difference between the points (1m, 0, 0) and (3m, 0, 0)? What
is the minimum work needed to move a +6µC charge between the two
points, starting from (1m, 0, 0)?
Since the electric potential is path independent (it comes from a conservative
force), we can integrate along any path we want; choose the
x-axis:
∫
∫3m
( )
∆V = − ⃗E · (îdx) = − 3 N
x 2 dx
C·m 2
( ) [
−→ ∆V = − 3 N x 3 ] 3
= −26 N·m
C·m 2 3
= −26V
1
C
N
1m
The work done by an external agent will be
W = −W E = q∆V = (6 × 10 −6 )(−26V) = −1.56 × 10 −4 J
Example
The figure below is a schematic representation of an electron “gun.”
A potential difference is maintained between the left and right plates,
with the right plate having a higher potential. By heating the left
plate, an electron is “boiled” off the plate. The electron, starting from
rest, then moves toward the right plate, directed toward a small hole in
the plate so that it “shoots” out of the gun. If the potential difference
between the plates is 9V, how fast will the electron be moving when it
reaches the right plate?
- +
s = ?
ΔV