Question

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 $y>>2a$. The charge $Q$ experiences and electrostatic force $F$. If $Q$ is now moved along the equatorial line to $P^{\prime }$ such that $O{P}^{\prime }=\left(\frac{y}{3}\right)$ , the force on $Q$ will be close to : $\left(\frac{y}{3}>>2a\right)$

• A. $\frac{F}{3}$
• B. 3 F
• C. 9 F
• D. 27 F

Answer 1

Answer: (D)

Electric field of equitorial plane of dipole
$=-\frac{K\vec{P}}{r^3}$
$\therefore AtP,F=\frac{K\vec{P}}{r^3}Q.$
$At{P}^1,F^1=-\frac{K\vec{P}Q}{{\left(r/3\right)}^3}=27F$