Two electrons each are fixed at a distance $2d$. A third charge proton placed at the midpoint is displaced slightly by a distance $x$ ($x \ll d$) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency: ($m$ = mass of charged…

Question

Two electrons each are fixed at a distance $2d$. A third charge proton placed at the midpoint is displaced slightly by a distance $x$ ($x \ll d$) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency: ($m$ = mass of charged particle)

Aicharya · Accepted Answer

From the given condition, we have F net &#160; q = - 2 F q / q cos &#952; F net &#160; q = - 2 &#183; 1 4 &#960; &#949; 0 &#183; q 2 d 2 + x 2 2 &#183; x d 2 + x 2 = - q 2 2 &#960; &#949; 0 x d 2 + x 2 3 / 2 For x &#60; &#60; d , F net &#160; q = - q 2 2 &#960; &#949; 0 &#160; d 3 x &#8756; &#160; &#160; a = - q 2 2 &#960; &#949; 0 &#183; m d 3 x Comparing with equation of SHM a = - &#969; 2 x &#8756; &#160; &#160; &#969; = q 2 2 &#960; &#949; 0 m d 3

Two electrons each are fixed at a distance $2d$. A third charge proton placed at the midpoint is displaced…

Solution