Two particles A and B , each carrying charge Q are held fixed with a separation D between them. A particle C having mass m and charge q is kept at the middle point of the line AB.
(a) If it is displaced throught a distance x perpendicular to AB, what would be the electric force experienced by it .
(b) Assuming x little, show that this force is proportional to x.
(c) under what conditions will the paricle C execute simple harmonic motion if it is released after such a small displacement? Find the time period of the oscillations if these conditions are stisfied.

Explanation

(a) From previous solution.
Net force acting
` =1/(2piepsilon_0) (qthetax)/[(d/x)^2+x^2]^(3/2) `
` (b) xltltd `
` the force =1/(2piepsilon_0)(qthetax)/((d/2)^3)=4/(piepsilon_0) (qthetax)/(d^3) `
` Force=mw^2x `
` 4/(piepsilon_0)(qthetax)/(d^3)=m((2pi)/T)^2x `
` or T^2=(mpi^3epsilon_0d^3)/(thetaq) `
` T=[(mpi^3epsilon_0d^3)/(thetaq)]^(1/2)`