Question

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^2$ and $ r^{ - 3} $
• B. p and $ r^{ - 2}$
• C. $ p^{ - 1} $ and $r^{ - 2}$
• D. p and $ r^{-3}$

Answer 1

Answer: (D)

he electric field at a point on equatorial line (perpendicular bisector) of dipole at a distance r is given by, E = $ \frac{ P}{ 4 \pi \varepsilon_0} \cdot \frac{1}{ (r^2 + a^2)^{ 3/2} } $
where 2 a = length of dipole $ ( \because$ r > > a)
$\therefore E = \frac{ P}{ 4 \pi \varepsilon_0} \cdot \frac{1}{ r^3 } \cdot $ i, e., E $ \propto$ p and E $ \propto r^{ - 3}$.