Question

For a short dipole at a point P on the equatorial line, where r ≫ a, the electric field is given by:

Options

• \[E_{eq} = \frac{1}{4\pi\varepsilon_0} \cdot \frac{p}{r}\]

• \[E_{eq} = \frac{1}{4\pi\varepsilon_0} \cdot \frac{p}{r^3}\]

• \[E_{eq} = \frac{1}{4\pi\varepsilon_0} \cdot \frac{p}{r^2}\]

• \[E_{eq} = \frac{1}{4\pi\varepsilon_0} \cdot \frac{2p}{r^3}\]

Answer 1

Through the derivation involving the geometry of the equatorial line and the approximation r ≫ a, the electric field at the equatorial line simplifies to \[E_{eq} = \frac{1}{4\pi\varepsilon_0} \cdot \frac{p}{r^3}\]. This is exactly half the magnitude of the axial field at the same distance, with direction opposite to the dipole moment.