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}}. $



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