Question

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

• A. $\left(\frac{1}{4 \pi \epsilon_0}\right) \frac{Q}{r^4}$
• B. $\left(\frac{1}{4 \pi \epsilon_0}\right) \frac{2 Q}{r^4}$
• C. $\left(\frac{1}{4 \pi \dot{\epsilon_0}}\right) \frac{3 Q}{r^4}$
• D. None of these

Answer 1

Answer: (C)

$ E=\frac{1}{4 \pi \epsilon_0}\left[\frac{2 p}{(r-\ell / 2)^3}-\frac{2 p}{(r+\ell / 2)^3}\right] $
$= \frac{1}{4 \pi \epsilon_0} \frac{3 Q}{r^4} $