  We study the decay process of $J/\psi\rightarrow e^+e^- \phi$ where the
relatively clean electromagnetic (EM) transitions appear at leading order at
tree level while the hadronic contributions only emerge via hadronic loop
transitions. We include the low-lying scalar $f_0(980)$ and pseudoscalar
$\eta/\eta'$ as the dominant contributions in the evaluation of the hadronic
loop contributions. It is found that the hadronic effects are negligible
comparing with the EM contributions. The decay width of $J/\psi\rightarrow
e^+e^- \phi$ is determined to be about $2.12\times 10^{-6}$ keV if there is no
any other leading mechanism contributing, and this result will be tested by the
BESIII experiment with a large data sample of $J/\psi$.
