83. The potential energy of the two-charge system is
U
=
1
4πε
0
q
1
q
2
(x
1
− x
2
)
2
+ (y
1
− y
2
)
2
=
8.99
× 10
9 N
·m
2
C
2
(3.0
× 10
−6
C)(
−4.0 × 10
−6
C)
(3.5 + 2.0)
2
+ (0.50
− 1.5)
2
cm
=
−1.9 J .
Thus,
−1.9 J of work is needed.
83. The potential energy of the two-charge system is
U
=
1
4πε
0
q
1
q
2
(x
1
− x
2
)
2
+ (y
1
− y
2
)
2
=
8.99
× 10
9 N
·m
2
C
2
(3.0
× 10
−6
C)(
−4.0 × 10
−6
C)
(3.5 + 2.0)
2
+ (0.50
− 1.5)
2
cm
=
−1.9 J .
Thus,
−1.9 J of work is needed.