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)

p and $r^{-3}$

Answer 2

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 $\propto r^{ - 3}$.