  Binary neutron star mergers are unique sources of gravitational waves in
multi-messenger astronomy. The inspiral phase of binary neutron stars can emit
gravitational waves as chirp signals. The present waveform models of
gravitational wave only considered the gravitational interaction. In this
paper, we derive the waveform of the gravitational wave signal taking into
account the presence of magnetic fields. We found that the electromagnetic
interaction and radiation can introduce different frequency-dependent power
laws for both amplitude and frequency of the gravitational wave. We show from
the results of Fisher information matrix that the third-generation observation
may detect magnetic dipole moments if the magnetic field is around 10^17 G.
