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.