Unification of fundamental forces is the dream of physics. Nevertheless, unfortunately gravitational force operators to be isolated in its geometrical content from other forces. This encourages some researchers to propose the so-called gravimagnetic field to unify gravity with other forces and to explain some cosmological problems at the early universe. This motivates to construct a new model to confirm the existence of gravitomagnetic and a corresponding magnetic field associated with any field. Using the formal Newton definition of force and considering the magnetic force to be related to the time varying mass, the magnetic force is shown to be equal to the centrifugal force. This equality is typical when treating a particle as string. Using also the definition of force in terms of potential and electric force only, energy is shown to be conserved. The Newton force can be defined also in terms of four-dimensional potential with the time varying part related to the magnetic potential. When the particle is treated as a string, energy conservation holds, while for ordinary particle, the Lagrangian is conserved. The energy conservation holds for special relativity also for energy per unit mass. The definition of acceleration for forces that obeys inverse square law shows also the magnetic force is equal to the centrifugal force.
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