Two small beads having positive charges q1 = 3q and q2 = q are fixed at the oppo

Question

Two small beads having positive charges q1 = 3q and q2 = q are fixed at the opposite ends of a horizontal insulating rod of length d = 1.50m. The bead with charge q1 is at the origin. as shown in figure p23.11, a third small, charged bead is free to slide on the rod. (a) at what position x is the third bead in equilibrium? (b) can the equilibrium be stable?

q1                 q2
+----------O----+ x
|<----x-->|
|<-------d----->|

thats what the picture looks like lol! The + sign is a ball with a positive sign in the middle. And the O is a ball and doesnt show a + or a -

Explanation / Answer

charge q1 =3q
charge, q2 =q
charge, q3 =q'
distance betweenthe charges = d
In equilibrium position,
Force between charges q1and q3 = Force between charges q2 and q3
( 9*109 Nm2/C2)( q1 q3 / r 2 ) = ( 9*10 9 Nm2/C2) [ q2 q3 / ( d- r ) 2 ]
( q1 / r2 ) = [ q2 / ( d - r ) 2 ]
( q1 / q2 ) = [ r/ ( d - r ) ] 2
        3 = [ r / ( d - r) ] 2
           [ r / ( d - r ) ] = 3
           r =3 d - 3 r
           r ( 1+ 3 ) = 3 d
           r = 0.634 d
              = (0.634)(1.5 m)
              = 0.951 m
.....................................................
yes ,
Equilibrium will be stable if the charges of same sign
as the other charges, i.e. positive.

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