Irodov Problem 3.41
Physics · electromagnetism
Problem
A point electric dipole with a moment p is placed in the external uniform electric field whose strength equals E0, with t t p E0. In this case one of the equipotential surfaces enclosing the dipole forms a sphere. Find the radius of this sphere.Intuitive explanation
The key insight is that a sphere becomes an equipotential when the potential from the external field exactly cancels the potential from the dipole at every point on that sphere's surface. Since the dipole moment is parallel to the field, the cancellation occurs along a specific direction—you need to find the radius where the dipole's potential magnitude equals the external field's potential, making the net potential constant around a spherical surface.
Intuitive explanation
The key insight is that a sphere becomes an equipotential when the potential from the external field exactly cancels the potential from the dipole at every point on that sphere's surface. Since the dipole moment is parallel to the field, the cancellation occurs along a specific direction—you need to find the radius where the dipole's potential magnitude equals the external field's potential, making the net potential constant around a spherical surface.