Question

The electrostatic potential at a general point at distance r from the center of a dipole, making an angle θ with the dipole axis (for r >> a), is:

Options

• \[V = \frac{p\cos\theta}{4\pi\varepsilon_0 r^2}\]

• \[V = \frac{p\cos\theta}{4\pi\varepsilon_0 r}\]

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

• \[V = \frac{p\sin\theta}{4\pi\varepsilon_0 r^2}\]

Answer 1

Substituting the first-order binomial approximations for 1/r₁ and 1/r₂ into V = (q/4πε₀)(1/r₁ − 1/r₂) gives V = (q/4πε₀)(2a cos θ/r²). Using p = 2qa, this becomes V = p cos θ/(4πε₀r²).