(a) Two charged particles , each charge `q`, are joined by an insultating string of length `L` and system is kept on smooth surface. Find tension in the string.
(b) A particle having charge `Q_(0)` is placed directly below and at separation `d` from the bob of simple pendulum at rest. The mass of the bob is `m`. What charge should be given to bob so that string becomes loose ?
( c) A particle `A` having charge `q` and mass `m` is placed at the bottom of a smooth inclined plane of inclination `theta`. Where should a block `B` , having same charge and mass , be placed on the incline so that it may remain in equilibrium ?

Explanation

(a) Since the net force on system is zero , system is at rest. Net force on each charge equal to zero.
`T = F_(e ) = (1)/( 4 pi in_(0)) (q^(2))/(L^(2))`
(b) `T = mg`
When bob is given a charge `q` , the weight of bob is balanced by repulsive electric force and not by tension in the string. Let charge `q` be given to bob.
`F_(e ) = mg`
`(1)/( 4 pi in_(0)) (qQ_(0))/(d^(2)) = mg`
`q = ( 4 pi in_(0) mgd^(2))/(Q_(0))`
(c ) Let block `B` be placed at distance `d`. The block `B` is in equilibrium . `mg cos theta` is balanced by normal reaction and `mg sin theta` by repulsive electric force.
`F_(e ) = mg sin theta`
`(1)/(4 pi in_(0)) (q^(2))/(d^(2)) = mg sin theta`
`d = q sqrt((1)/(4 pi in_(0) mg sin theta))`