Q 12-01-140JEE MainJEE Main 2019 (10 Jan, Shift 2)Easy
Charges $-q$ and $+q$, located at $A$ and $B$, respectively, constitute an electric dipole. Distance $AB = 2a$, $O$ is the mid point of the dipole and $OP$ is perpendicular to $AB$. A charge $Q$ is placed at $P$ where $OP = y$ and $y \gg 2a$. The charge $Q$ experiences an electrostatic force $F$. If $Q$ is now moved along the equatorial line to $P'$ such that $OP' = \dfrac y3$, the force on $Q$ will be close to $\left(\dfrac y3 \gg 2a\right)$
Answer: (A) $27F$
Far from the dipole on its equatorial line, $E = \dfrac{kp}{r^3}$, so $F = QE \propto \dfrac1{r^3}$.
Reducing the distance to one third multiplies the force by $3^3 = 27$: the new force is $27F$.
Solution by Sreeraj P, M.Sc Physics