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Q.
For distance far away from centre of dipole the change in
magnitude of electric field with change in distance from
the centre of dipole is
Electric Charges and Fields
Solution:
For distances far away from centre of dipole
$ E _{ axis }= E _{ a }=\frac{1}{4 \pi \varepsilon_0} \frac{2 p }{ r ^3} $
$ E _{\text {equa }}= E _{ e }=\frac{1}{4 \pi \varepsilon_0}-\frac{ p }{ r ^3} $
$\frac{ d }{ dr }\left( E _{ a }\right)=\frac{1}{4 \pi \varepsilon_0} 2 p \frac{ d }{ dr }\left( r ^{-3}\right)=-6 \cdot \frac{1}{4 \pi \varepsilon_0} \frac{ p }{ r ^4} $.....(i)
$\frac{ d }{ dr }\left( E _{ c }\right)=\frac{1}{4 \pi \varepsilon_0} p \frac{ d }{ dr }\left( r ^{-3}\right)=-3 \frac{1}{4 \pi \varepsilon_0} \frac{ p }{ r ^4}$....(ii)
From equations (i) and (ii) the magnitude of change in electric field w.r.t. distance is more in case of axis of dipole as compared to equatorial plane.