الفيزياء العامة الجزء الثاني#موقع الفيزياء.كوم

Lectures in General Physics
5.4 Potential difference due to a point charge
Assume two points A and B near to a positive charge q as shown in figure
5.7. To calculate the potential difference V B -V A we assume a test charge q o
is moved without acceleration from A to B.
F Ddl
E B Oq o
E A
Oq o
Rr
Figure 5.7
In the figure above the electric field E is directed to the right and dl to the
left.
r r
ο
E.
dl = E cos180 dl = −Edl
(5.10)
However when we move a distance dl to the left, we are moving in a
direction of decreasing r. Thus
r r
dl = −dr
(5.11)
Therefore
-Edl=Edr (5.12)
∴V
B
−V
A
B
r
r r
B
r r
= −∫ E. dl = E.
d
(5.13)
A
Substitute for E
1 q
Q E =
2
4πε ο r
(5.14)
∫
rA
We get
Dr. Hazem Falah Sakeek