Question

The exact potential on the axial line of a dipole with half-length l, before applying the approximation \[r \gg l\], is:

Options

• \[V = \frac{1}{4\pi\varepsilon_0}\frac{p}{r^2 - l^2}\]

• \[V = \frac{1}{4\pi\varepsilon_0}\frac{p}{r^2 + l^2}\]

• \[V = \frac{1}{4\pi\varepsilon_0}\frac{p}{r^2 - l}\]

• \[V = \frac{1}{4\pi\varepsilon_0}\frac{2p}{r^2 - l^2}\]

Answer 1

Adding the potentials algebraically: V = kq/(r − l) − kq/(r + l) = kq(2l)/(r² − l²). Since the dipole moment is p = 2ql, this simplifies to V = kp/(r² − l²). When r >> l, the l² term becomes negligible and V → kp/r².