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(D) The electric field on the axis of a dipole at distance $x$ is given by $E_{	ext{axis}} = \frac{1}{4\pi\epsilon_0} \cdot \frac{2p}{x^3}$.The elect

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$\sqrt[3]{2}:1$

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(D) The electric field on the axis of a dipole at distance $x$ is given by $E_{	ext{axis}} = \frac{1}{4\pi\epsilon_0} \cdot \frac{2p}{x^3}$.The electric field on the equatorial line of a dipole at distance $y$ is given by $E_{	ext{equatorial}} = \frac{1}{4\pi\epsilon_0} \cdot \frac{p}{y^3}$.Given that $E_{	ext{axis}} = E_{	ext{equatorial}}$,we have:$\frac{2p}{x^3} = \frac{p}{y^3}$.Simplifying the equation:$\frac{2}{x^3} = \frac{1}{y^3} \Rightarrow \frac{x^3}{y^3} = 2$.Taking the cube root on both sides:$\frac{x}{y} = \sqrt[3]{2} = 2^{1/3}$.Therefore,the ratio $x:y$ is $\sqrt[3]{2}:1$.

If the electric field intensity at a distance $x$ on the axis of a dipole is equal to the electric field intensity at a distance $y$ on its equatorial line,then the ratio $x:y$ is:

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