الفيزياء العامة الجزء الثاني#موقع الفيزياء.كوم

Electric Potential Difference
The relation in general case (not uniform electric field):
If the test charge q o is moved along a curved path from A to B as shown in
figure 5.5. The electric field exerts a force q o E on the charge. To keep the
charge moving without accelerating, an external agent must apply a force F
equal to -q o E.
If the test charge moves distance dl
along the path from A to B, the work
done is F.dl. The total work is given
by,
B
F
Ddl
Oq o
W
AB
=
B
∫
A
r r
B
r r
F. dl = −q
E.
dl
(5.4)
∫
o
A
The potential difference V B -V A is,
Oq o
E
A
V
B
−V
A
W
=
q
AB
o
B
= −∫
A
r
E dl
r
. (5.5)
لاحظ هنا أن حدود التكامل من
E
Figure 5.5
dl
إلى B
هى التي تحدد المسار ومنه اتجاه متجه
الإزاحة
A
وتكون الزاوية θ
هي الزاوية المحصورة بين منتجه الإزاحة ومتجه المجال الكهربي.‏
If the point A is taken to infinity then V A =0 the potential V at point B is,
V
B
B
= −
∫
∞
r r
E . dl
(5.6)
This equation gives the general relation between the potential and the
electric field.
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