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. If particle C is displaced through a distance x along the line AB. What will be the time period of the oscillations.

Explanation

Net force
` =1/(4piepsilon_0)[[d theta)/((d/2)+x)^2-(d theta)/((d/2)-x)^2] `
` =(d theta)/(4piepsilon_0)[[(d/2)^2+x^2-xd-(d/2)^2-x^2-xd]/[(d/2)^2-x^2]^2] `
` So, net force=(q theta)/(4piepsilon_0)-(-2xd)/(d^4) `
` =(-q theta)/(4piepsilon_0)x/d^3 `
` or m((2pi)/T)^2=(q theta)/(4piepsilon_0d^3) `
` T=[(pi^3epsilon_0md^3)/(2 theta q)]^(1/2)`.