A unit negative charge with mass M resides at the mid-point of the straight line of length 2 a adjoining two fixed charges of magnitude + Q each. If it is given a very small displacement x ( x

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

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From figure the net force F bet ​ F net ​ ​ = − F cos θ + ( − F cos θ ) = − 2 F cos θ = − 2 × ( x 2 + a 2 ) k Q × 1 ​ × x 2 + a 2 ​ x ​ = − ( x 2 + a 2 ) 3/2 2 k Q ​ ⋅ x = − ( a 3 2 k Q ​ ) ⋅ x ​ Frequency of oscillation = 2 π 1 ​ M a 3 2 k Q ​ ​ = 2 π 1 ​ M a 3 2 × 4 π ε 0 ​ 1 ​ ⋅ Q ​ ​ = 2 π 1 ​ 2 π e 0 ​ M a 3 Q ​ ​ ⇒ ( ∗ None of the option matches)

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