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An electric dipole with dipole moment (p0/sqrt(2))(i + j) is fixed at the origin O in a uniform external electric field of magnitude E0. The potential is found to be constant on a circle of radius R centered at O (R >> dipole size). Which of the following is/are correct? (e0 = permittivity of free space) [JEE-Advanced 2019]

1. R = (p0/(4*pi*e0*E0))^(1/3)
2. The magnitude of the total electric field at any two points on the circle is the same
3. Total electric field at point A is E_A = sqrt(2)*E0*(i + j)
4. Total electric field at point B is E_B = 0

Correct answer: R = (p0/(4*pi*e0*E0))^(1/3)

Solution

The dipole moment points along (i + j)/sqrt(2). The uniform field E0 combines with the dipole field. The circle is the zero-potential / constant-potential locus where the dipole's contribution along the axis balances the external field. Setting k*2p0/R³ type balance gives R = (p0/(4*pi*e0*E0))^(1/3). This is the official correct option (A) for the JEE-Advanced 2019 problem. The total field is not uniform on the circle, and the specific field expressions in C and B do not hold in general; A is the established correct answer.

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