Unformatted text preview: al, choose U = 0 to be at infinity:
Case A q2 1
UA =
4πε 0 d d Case B q1q2 1
U (r ) =
4πε 0 r 2d q2 1
UB =
4πε 0 2d U(r) UA > UB
0
0 23 r
r U(d)
U(2d) Preflight 2
Preflight 2
60 BB 50
40
30
20
10
0 A
B
C
D
E Change in potential energy equals the final
potential energy minus the initial potential energy.
To represent this, the expression((1/r2)(1/r1)) is
needed. This expression multiplied by kQq gives
the change in potential energy.
Since it is a change in potential energy, it must
contain both r1 and r2, and since r1 is smaller
than than r2, we subtract 1/r2 from 1/r1
34 U1 = 1 Qq
4πε 0 r1 ∆U ≡ U 2 − U 1 = U2 = 1 Qq
4πε 0 r2 Qq 1 1 −
4πε 0 r2 r1 Potential Energy of Many Charges
Two charges are separated by a distance d. What is the change in potential energy when a third charge q is brought from far away to a distance d from the original two charges? Q2 d qQ1 1 qQ2 1
∆U =
+
4πε 0 d 4πε 0 d
(superposition) d q Q1 d 25 Potential Energy of Many Charges
What is the total energy required to bring in three identical charges, from infinitely far away to the points on an equilateral triangle shown. A) 0
B) Q1
4πε 0 d
C) Q2 1
∆U = 2
4πε 0 d
D) Q2 1
∆U = 3
4πε 0 d
E) Q2 1
∆U = 6
4πε 0 d
∆U = Q 2 d Q Work (by E) to bring in third charge : 27 3 Q2
W = ∑ Wi = −
4πε 0 d d d Work (by E field) to bring in first charge: W1 = 0
Work (by E field) to bring in second charge : BB Q 3 Q2
∆U = +
4πε 0 d Q2
W2 = −
4π 0 d
ε
1 Q2
1 Q2
2 Q2
W3 = −
−
=−
4πε0 d
4πε0 d
4πε0 d
1 Potential Energy of Many Charges
Suppose one of the charges is negative. Now what is the total energy required to brin...
View
Full Document
 Spring '14
 Energy, Potential Energy, Electric charge

Click to edit the document details