P22_008.PDF

8. With rightwards positive, the net force on q 3 is

k q 1 q 3

d 2

We note that each term exhibits the proper sign (positive for rightward, negative for leftward) for all

possible signs of the charges. For example, the ﬁrst term (the force exerted on q 3 by q 1 ) is negative if

they are unlike charges, indicating that q 3 is being pulled toward q 1 , and it is positive if they are like

charges (so q 3 would be repelled from q 1 ). Setting the net force equal to zero and canceling k , q 3 and

d 2 leads to

⇒

q 1 =

−

4 q 2 .

(2 d ) 2 + k q 2 q 3

q 1

4 + q 2 =0 =