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Electric Potential Difference
5.7 Electric Potential Energy
The definition of the electric potential energy of a system of charges is the
work required to bring them from infinity to that configuration.
To workout the electric potential energy for a system of charges, assume a
charge q 2 at infinity and at rest as shown in figure 5.11. If q 2 is moved from
infinity to a distance r from another charge q 1 , then the work required is
given by
W=Vq 2
1 q1
Q V =
4πε ο r
Substitute for V in the equation of work
U
1 q q
4πε ο r
1 2
= W =
(5.20)
12
q1q
2
U = (5.21)
4πε ο r
To calculate the potential energy for systems containing more than two
charges we compute the potential energy for every pair of charges
separately and to add the results algebraically.
qi
qj
U = ∑
4πε ο rij
(5.22)
القانون الأول يطبق في حالة شحنتين فقط،‏ ولكن إذا كانت المجموعة المراد إيجاد طاقة الوضع
الكهربي لها أكثر من شحنتين نستخدم القانون الثاني حيث نوجد الطاقة المختزنة بين كل شحنتين
على حده
ثم نجمع جمعا جبريا،‏
أي
نعوض عن قيمة الشحنة ونأخذ الإشارة بالحسبان
كل في
q 1 q 2
If the total electric potential energy of a system of charges is positive this
correspond to a repulsive electric forces, but if the total electric potential
energy is negative this correspond to attractive electric forces. (explain
why?)
r
Figure 5.11
مرة.‏
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