Question

Two small beads having positive charges q1 = 28q and q2 = q are fixed at the opposite ends of a horizontal insulating rod of length d = 1.50 m. The bead with charge q1 is at the origin. As shown in the figure below, a third small, charged bead is free to slide on the rod.

Answer 1

charge q1 = 28q

charge, q2 = q

charge, q3 = q'

distance between the charges, d = 1.5 m

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

28 = [ r / ( d - r) ] ²

  [ r / ( d - r ) ] = √28

r =√28d - √28r

r ( 1+ √28 ) = √28d

r = 0.84 d = (0.84)(1.5 m) = 1.26 m

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