The magnetic radiation reaction force is a force on an electromagnet when its magnetic moment changes. One can derive an electric radiation reaction force for an accelerating charged particle caused by the particle emitting electromagnetic radiation. Likewise, a magnetic radiation reaction force can be derived for an accelerating magnetic moment emitting electromagnetic radiation. Similar to the electric radiation reaction force, three conditions must be met in order to derive the following formula for the magnetic radiation reaction force. First, the motion of the magnetic moment must be periodic, an assumption used to derive the force. Second, the magnetic moment is traveling at non-relativistic velocities (that is, much slower than the speed of light). Finally, this only applies this force is proportional to the fifth derivative of the position as a function of time (sometimes somewhat facetiously referred to as the "Crackle"). Unlike the Abraham–Lorentz force, the force points in the direction opposite of the "Crackle". Definition and description Mathematically, the magnetic radiation reaction force is given by, in SI units: where: is the force, is the Pop (the third derivative of acceleration, or the fifth derivative of displacement), is the permeability of free space, is the speed of light in free space is the electric charge of the particle. is the radius of the magnetic moment Note that this formula applies only for non-relativistic velocities. Physically, a time changing magnetic moment emits radiation similar to the Larmor formula of an accelerating charge. Since momentum is conserved, the magnetic moment is pushed in the direction opposite the direction of the emitted radiation. In fact the formula above for radiation force can be derived from the magnetic version of the Larmor formula, as shown below. Background In classical electrodynamics, problems are typically divided into two classes: Problems in which the charge and current sources of fields are specified and the fields are calculated, and The reverse situation, problems in which the fields are specified and the motion of particles are calculated. In some fields of physics, such as plasma physics and the calculation of transport coefficients (conductivity, diffusivity, etc.), the fields generated by the sources and the motion of the sources are solved self-consistently. In such cases, however, the motion of a selected source is calculated in response to fields generated by all other sources. Rarely is the motion of a particle (source) due to the fields generated by that same particle