An electric dipole with dipole moment 𝐩 = (p₀/√2)( $\hat{i}+\hat{j}$ ) is fixed at the origin O in a uniform electric field of magnitude E₀. If the potential is constant on a circle of radius R centred at O as shown, which statement(s) is/are correct? (R is much larger than dipole size.)
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Question

An electric dipole with dipole moment 𝐩 = (p₀/√2)( $\hat{i}+\hat{j}$ ) is fixed at the origin O in a uniform electric field of magnitude E₀. If the potential is constant on a circle of radius R centred at O as shown, which statement(s) is/are correct? (R is much larger than dipole size.)

Select all that apply

G1 Physics · Accepted Answer

Step 1: The external potential is -E₀r cosθ relative to the field direction, while dipole potential is (1/4πε₀)(p₀ cosθ/r²). For a circle to be equipotential, their angular coefficients cancel, giving R³=p₀/(4πε₀E₀), so A is true. Step 2: Evaluate the total field at the marked points using the dipole field 𝐄d=(1/4πε₀R³)[3(𝐩·𝐞ᵣ)𝐞ᵣ-𝐩]. Step 3: At B it exactly cancels the uniform field, so D is true; the other statements are false. Final: A, D.