Dipole in a uniform electric field

JEE Advanced 2019 Paper 2, Question 4

An electric dipole with dipole 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 centered at the origin as shown in figure, then the correct statement(s) is/are:

(\varepsilon_{0} is permittivity of free space. R \gg dipole size)

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  1. R=\left(\frac{p_{0}}{4 \pi \epsilon_{0} E_{0}}\right)^{1 / 3}
  2. Total electric field at point A is {\bf E}^A=\sqrt{2} E_{0}(\hat{i}+\hat{j})
  3. Total electric field at point B is {\bf E}^B=0
  4. The magnitude of total electric field on any two points of the circle will be same.


The potential due to the dipole kept at the origin …

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