Biomedical Engineering Reference
In-Depth Information
and examination of Figure 1.6 shows that d
l
cos θ is the radial distance moved by charge
q
, which we will write d
r
.
q
Point I
d
l
r
Q
r
+
d
l
Origin
Point II
Figure 1.5
Electrostatic work
F
q
θ
d
l
r
Origin
Figure 1.6
Relationship between vectors
Hence
Qq
r
2
d
r
The total work done moving from position I to position II is therefore found by integrating
1
4πε
0
d
w
on
=−
II
1
4πε
0
Qq
r
2
d
r
w
on
=−
(1.8)
I
4πε
0
Qq
1
1
1
r
I
=
r
II
−
The work done depends only on the initial and final positions of charge
q
; it is independent
of the way we make the change.
Another way to think about the problem is as follows. The force is radial, and we can
divide the movement from position I to position II into infinitesimal steps, some of which
are parallel to
F
and some of which are perpendicular to
F
. The perpendicular steps count
0 towards
w
on
, the parallel steps only depend on the change in the (scalar) radial distance.
