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An electric dipole with moment $\frac{p_{0}}{\sqrt{2}} (\hat{i} + \hat{j})$ is held fixed at the origin O in the presence of an uniform electric field of magnitude $E_{0}$ . If the potential is constant on a circle of radius R centred at the origin as shown in figure, then the correct statement(s) is/are : ( $ε_{0}$ is permittivity of free space. R>>dipole size)

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An Intiative by Sri Chaitanya

the magnitude of total electric field on any two points of the circle will be same

Total electric field at point B is ${\vec{E}}_{B} = \vec{0}$

Total electric field at point A is ${\vec{E}}_{A} = \sqrt{2} E_{0} (\hat{i} + \hat{j})$

$R = {(\frac{p_{0}}{4 π \in_{0} E_{0}})}^{1 / 3}$

answer is B, D.

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Tangential electric field is zero

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