Question

In the binomial-approximation derivation of the dipole potential, which order of terms in \[a/r\] is retained throughout the calculation?

Options

• Only first-order terms in \[a/r\]

• Only zeroth-order terms, discarding \[a/r\] entirely

• Terms up to second order in \[a/r\]

• All orders in \[a/r\]

Answer 1

Because r >> a, higher powers of a/r are negligibly small. Retaining only first-order terms — both when simplifying r₁² and r₂² and when applying the Binomial theorem — yields the standard result V = p cos θ/(4πε₀r²).