Question

Figure shows an electric quadrupole, with quadrupole moment $\left(Q=2q{\ell }^2\right)$. The electric field at a distance from its centre at the axis of the quadrupole is given by

• A. $\left(\frac{1}{4\pi {ϵ}_0}\right)\frac{Q}{r^4}$
• B. $\left(\frac{1}{4\pi {ϵ}_0}\right)\frac{2Q}{r^4}$
• C. $\left(\frac{1}{4\pi \dot{{ϵ}_0}}\right)\frac{3Q}{r^4}$
• D. None of these

Answer 1

Answer: (C)

$E=\frac{1}{4\pi {ϵ}_0}\left[\frac{2p}{(r-\ell /2{)}^3}-\frac{2p}{(r+\ell /2{)}^3}\right]$
$=\frac{1}{4\pi {ϵ}_0}\frac{3Q}{r^4}$