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Statement I: The electric field due to a dipole on its axial line at a distance r is E. Then, electric field due to the same dipole on the equatorial line and at the same distance will be $\frac{E}{2}$ .
Statement II: Electric field due to dipole varies inversely as the square of distance.

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Both statements I and II are correct

Statement-I is correct and statement-II is incorrect

Statement-I is incorrect and statement-II is correct

Both statements I and II are incorrect

answer is B.

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Detailed Solution

We know that for an electric dipole,

$E_{axial} = \frac{1}{4 {πε}_{0}} (\frac{2 p}{r^{3}}) and E_{equatorial} = \frac{1}{4 {πε}_{0}} (\frac{p}{r^{3}})$

Hence, from above equations,

$\frac{E_{axial}}{2} = E_{equatorial} Hence, E_{equatorial} = \frac{E}{2}$

Statement II is false as electric field due to dipole varies inversely as cube of distance, i.e., $E \propto \frac{1}{r^{3}} .$

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