الفيزياء العامة الجزء الثاني#موقع الفيزياء.كوم

Lectures in General Physics
Example 5.13
Derive an expression for the work
required to put the four charges together
as indicated in figure 5.16.
Q+q
Aa
Aa
Q-q
Aa
Solution
The work required to put these charges
together is equal to the total electric potential
energy.
Q-q
Aa
Figure 5.16
Q+q
U = U 12 + U 13 + U 14 + U 23 + U 24 + U 34
U
=
1 ⎡−
q
4πε ⎢
ο ⎣ a
2
+
q2
q
−
2a
a
2
q
−
a
2
+
q2
q2⎤
−
a
⎥
2a
⎦
U
=
⎡−
4q
4πε ⎢
ο ⎣ a
1
2 2
2q
⎤
+ ⎥
2a
⎦
U
=
1 ⎡ − 24q
2 + 2q2⎤
− 0. 2 q
⎢
⎥ =
4πε ο ⎣ 2a
⎦ ε ο
a
2
The minus sign indicates that there is attractive force between the charges
In Example 5.13 assume that if all the charges are positive, prove that
the work required to put the four charges together is
2
1 5.41q
U =
4πε ο
ε ο
a
Dr. Hazem Falah Sakeek