Charges - q and + q , located at A and B , respectively, constitute an electric dipole. Distance A B = 2 a , O is the mid point of the dipole and O P is perpendicular to A B . A charge Q is placed at

Question

Charges - q and + q , located at A and B , respectively, constitute an electric dipole. Distance A B = 2 a , O is the mid point of the dipole and O P is perpendicular to A B . A charge Q is placed at P where O P = y and y ≫ 2 a . The charge Q experiences an electrostatic force F . If Q is now moved along the equatorial line to P ' such that O P ' = y 3 the force on Q will be close to y 3 ≪ 2 a

TestHub · Accepted Answer

Electric field intensity at the distance $y$ along the perpendicular bisector is

$|E_{1}| = \frac{K P}{y^{3}}$

So, force at distance $y$ on $Q$ ,

$F = Q (E_{1}) = Q (\frac{K P}{y^{3}})$ ... $(1)$

$F' = Q \frac{K P}{{(\frac{y}{3})}^{3}}$ ... $(2)$

Dividing $(1)$ by $(2)$ , we get,

$\frac{F'}{F} = {(3)}^{3}$

$∴ F' = 27 F$

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