If a charged particle is moving along a magnetic field line, that means it is moving either parallel or anti parallel to the direction of magnetic field. i.e. the direction of velocity of the particle is either making an angle of 0 or ϖ. According to F = qvBsinϴ (where q is the charge of the particle, v is the velocity of it and B is the magnitude of the external Magnetic field and ϴ is the angle between the direction of magnetic field and the velocity) for ϴ = 0 or ϖ, F= 0.