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  4. The electric field due to a short electric dipole at a distance r on the axial line from its mid-point is x times the electric field at a distance 2 r on the equatorial line from the mid-point of dipole. Then, the value of x is

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Q. The electric field due to a short electric dipole at a distance $r$ on the axial line from its mid-point is $x$ times the electric field at a distance $2 r$ on the equatorial line from the mid-point of dipole. Then, the value of $x$ is

AP EAMCETAP EAMCET 2018

Solution:

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On axis, field magnitude, $E_{1}=\frac{2 k p}{r^{3}}$
On equatorial axis, field magnitude
$E_{2}=\frac{k p}{(2 r)^{3}}=\frac{k p}{8 r^{3}}$
So, $E_{1}=16 E_{2}$
$ \Rightarrow x=16$