Electrostatics Question 716
Question: An electric quadrupole, with quadruple moment $ (Q=2q{{\ell }^{2}}). $ The electric field at a distance from its center at the axis of the quadrupole is given by
Options:
A) $ ( \frac{1}{4\pi {\in _{0}}} )\frac{Q}{r^{4}} $
B) $ ( \frac{1}{4\pi {\in _{0}}} )\frac{2Q}{r^{4}} $
C) $ ( \frac{1}{4\pi {\in _{0}}} )\frac{3Q}{r^{4}} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ E=\frac{1}{4\pi {\in _{0}}}[ \frac{2p}{{{( r-\ell /2 )}^{3}}}-\frac{2p}{{{( r+\ell /2 )}^{3}}} ] $
$ =\frac{1}{4\pi {\in _{0}}}\frac{3Q}{r^{4}}. $
