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Question

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

Vedclass · Accepted Answer

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

Vedclass · Answer

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

If the magnitude of the intensity of the electric field at a distance $x$ on the axial line and at a distance $y$ on the equatorial line for a given electric dipole are equal,then the ratio $x:y$ is:

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