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A unit negative charge with mass resides...

A unit negative charge with mass resides at the midpoint of the straight line of length 2a adjoining two fixed charges of magnitude `+Q` each. If it is given a very small displacement `x(x lt lt a)` in a direction perpendicular to the straight line, it will

A

come back to its original position and stay there

B

excute oscillations with freqeuncy `(1)/(2pi) sqrt((Q)/(4pi epsi_(0) Ma^(3)))`

C

fly to infinity

D

execute oscillations with frequency `(1)/(2pi) sqrt(( Q)/(2pi epsi_(0) Ma^(3)))`

Text Solution

Verified by Experts

`F_("net") =- 2 F cos theta= -2 (KQxx1)/( (x^(2)+a^(2)))xx(x)/( sqrt(x^(2)+a^(2)))`
`=(-2kQ)/((x^(2)+a^(2))^((3)/(2)))x`
`:. F_("net") ~~-((2KQ)/(a^(3))) x[ :. xlt lt a]`

Frequency of oscillation
`(1)/(2pi) sqrt((2kQ)/(Ma^(3)))=(1)/(2pi) sqrt((2xx (1)/(4 pi epsi_(0))Q)/(Ma^(3)))=(1)/(2pi) sqrt((Q)/(2pi epsi_(0) Ma^(3)))`
[frequency of SHM. `n=(1)/(2pi) sqrt(("acceleration")/("displacement"))]`
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