a unit vector pointing along the line from M to m, and G is Newton's gravitational constant. Therefore, the gravitational field of M is The experimental observation that inertial mass and gravitational mass are equal to unprecedented levels of accuracy leads to the identification of the gravitational field strength as identical to the acceleration experienced by a particle. This is the starting point of the equivalence principle, which leads to general relativity. For a discrete collection of masses, Mi, located at points, ri, the gravitational field at a point r due to the masses is If we have a continuous mass distribution ρ instead, the sum is replaced by an integral, Note that the direction of the field points from the position r to the position of the masses ri; this is ensured by the minus sign. In a nutshell, this means all masses attract. In the integral form Gauss's law for gravity is while in differential form it is Therefore, the gravitational field g can be written in terms of the gradient of a gravitational potential : This is a consequence of the gravitational force F being conservative. Electromagnetism Electrostatics A charged test particle with charge q experiences a force F based solely on its charge. We can similarly describe the electric field E generated by the source charge Q so that : Using this and Coulomb's law the electric field due to a single charged particle is The electric field is conservative, and hence is given by the gradient of a scalar potential, Gauss's law for electricity is in integral form while in differential form Magnetostatics A steady current I flowing along a path ℓ will exert a force on nearby charged particles that is quantitatively different from the electric field force described above. The force exerted by I on a nearby charge q with velocity v is where B(r) is the magnetic field, which is determined from I by the Biot–Savart law: The magnetic field is not conservative in general, and hence cannot usually be written in terms of a scalar potential. However, it can be written in terms of a vector potential, A(r): Gauss's law for magnetism in integral form is while in differential form it is The physical interpretation is that there are no magnetic monopoles. Electrodynamics In general, in the presence of both a charge density ρ(r, t) and current density J(r, t), there