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The validity of Ampère's model means that it is allowable to think of the magnetic material as if it consists of current-loops, and the total effect is the sum of the effect of each current-loop, and so the magnetic effect of a real magnet can be computed as the sum of magnetic effects of tiny pieces of magnetic material that are at a distance ...
The magnetic force component of the Lorentz force manifests itself as the force that acts on a current-carrying wire in a magnetic field. In that context, it is also called the Laplace force . The Lorentz force is a force exerted by the electromagnetic field on the charged particle, that is, it is the rate at which linear momentum is ...
Lorentz force on a charged particle (of charge q) in motion (velocity v), used as the definition of the E field and B field. Here subscripts e and m are used to differ between electric and magnetic charges. The definitions for monopoles are of theoretical interest, although real magnetic dipoles can be described using pole strengths.
Maxwell's equations are partial differential equations that relate the electric and magnetic fields to each other and to the electric charges and currents. Often, the charges and currents are themselves dependent on the electric and magnetic fields via the Lorentz force equation and the constitutive relations.
where is the magnetic force constant from the Biot–Savart law, / is the total force on either wire per unit length of the shorter (the longer is approximated as infinitely long relative to the shorter), is the distance between the two wires, and , are the direct currents carried by the wires.
The same situations that create magnetic fields—charge moving in a current or in an atom, and intrinsic magnetic dipoles—are also the situations in which a magnetic field has an effect, creating a force. Following is the formula for moving charge; for the forces on an intrinsic dipole, see magnetic dipole.
Using the definition of the cross product, the magnetic force can also be written as a scalar equation: [10]: 357 = where F magnetic, v, and B are the scalar magnitude of their respective vectors, and θ is the angle between the velocity of the particle and the magnetic field.
This demonstrates that the force is the same in both frames (as would be expected), and therefore any observable consequences of this force, such as the induced current, would also be the same in both frames. This is despite the fact that the force is seen to be an electric force in the conductor frame, but a magnetic force in the magnet's frame.