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 waves 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 the amplitude and frequency of the gravitational wave. We show from the results of the Fisher information matrix that the third-generation observation may detect magnetic dipole moments if the magnetic field is ∼1017 G.

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