Question

1 if the magnitude of intensity of electric field at a distance x on axial line and at a distance y on equatorial line on a given dipole are equal, then x : y is (a) 1 : 1 (b) 1 : (c) 1 : 2 (d)

Answer 1

your question is -> if the magnitude of intensity of electric field at a distance x on axial line and at a distance y on equatorial line on a given dipole are equal, then x : y is (a) 1 : 1 (b) 1 : (c) 1 : 2 (d) $\sqrt[3]{2}$ : 1

answer : option (d) $\sqrt[3]{2}$ : 1

explanation : we know, magnitude of electric field due to dipole on axial line is given by, $E_{\textbf{axial}}=\frac{2kp}{x^3}$

and magnitude of electric field due to dipole at a point on equatorial line is given by, $E_{\textbf{equatorial}}=\frac{kp}{y^3}$

a/c to question,

$E_{\textbf{axial}}=E_{\textbf{equatorial}}$

or, 2kp/x³ = kp/y³

or, 2/x³ = 1/y³

or, $\frac{x}{y}=\frac{\sqrt[3]{2}}{1}$

hence, option (D) is correct choice.