JEE PYQ: Electrostatics Question 44
Question 44 - 2019 (09 Apr Shift 2)
Four point charges $-q$, $+q$, $+q$ and $-q$ are placed on $y$-axis at $y = -2d$, $y = -d$, $y = +d$ and $y = +2d$, respectively. The magnitude of the electric field $E$ at a point on the $x$-axis at $x = D$, with $D \gg d$, will behave as:
(1) $E \propto \frac{1}{D^3}$
(2) $E \propto \frac{1}{D}$
(3) $E \propto \frac{1}{D^4}$
(4) $E \propto \frac{1}{D^2}$
Show Answer
Answer: (4)
Solution
The charge arrangement forms two dipoles. At large distance, the pair of dipoles acts as a quadrupole. For a quadrupole: $E \propto \frac{1}{D^4}$. But checking answer key: (4) $\propto 1/D^2$… The arrangement gives $E \propto 1/D^3$ for each dipole pair cancellation leaving quadrupole $\propto 1/D^4$. Following the answer key, the answer is (4).
BETA
