Electric Charges and Fields - Result Question 28
28. A point $Q$ lies on the perpendicular bisector of an electrical dipole of dipole moment $p$. If the distance of $Q$ from the dipole is $r$ (much larger than the size of the dipole), then the electric field at $Q$ is proportional to
(a) $p^{-1}$ and $r^{-2}$
(c) $p^{2}$ and $r^{-3}$
(b) $p$ and $r^{-2}$
(d) $p$ and $r^{-3}$
[1998]
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Answer:
Correct Answer: 28. (d)
Solution:
- (d) Electric field at equatorial point
$ E e q=\frac{1 p}{4 \pi E_o(r^{2}+l^{2})^{3 / 2}} $
$ E=\frac{p}{4 \pi \varepsilon_0 \cdot r^{3}} \quad[\text{ For } \quad r»l] $
Apparently, $E \propto p$ and $E \propto \frac{1}{r^{3}} \propto r^{-3}$.
