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where is back EMF, is the constant, is the flux, and is the angular velocity. By Lenz's law, a running motor generates a back-EMF proportional to the speed. Once the motor's rotational velocity is such that the back-EMF is equal to the battery voltage (also called DC line voltage), the motor reaches its limit speed.
Faraday's law is a single equation describing two different phenomena: the motional emf generated by a magnetic force on a moving wire (see the Lorentz force), and the transformer emf generated by an electric force due to a changing magnetic field (described by the Maxwell–Faraday equation).
The electromotive force generated by motion is often referred to as motional emf. When the change in flux linkage arises from a change in the magnetic field around the stationary conductor, the emf is dynamically induced. The electromotive force generated by a time-varying magnetic field is often referred to as transformer emf.
Position vector r is a point to calculate the electric field; r′ is a point in the charged object. Contrary to the strong analogy between (classical) gravitation and electrostatics, there are no "centre of charge" or "centre of electrostatic attraction" analogues. [citation needed] Electric transport
The emf generated by Faraday's law of induction due to relative movement of a circuit and a magnetic field is the phenomenon underlying electrical generators. When a permanent magnet is moved relative to a conductor, or vice versa, an electromotive force is created.
That is, the back-EMF is also due to inductance and Faraday's law, but occurs even when the motor current is not changing, and arises from the geometric considerations of an armature spinning in a magnetic field. This voltage is in series with and opposes the original applied voltage and is called "back-electromotive force" (by Lenz's law).
Electric field from positive to negative charges. Gauss's law describes the relationship between an electric field and electric charges: an electric field points away from positive charges and towards negative charges, and the net outflow of the electric field through a closed surface is proportional to the enclosed charge, including bound charge due to polarization of material.
The galvanometer usually only measures the first term in the EMF which contributes the current in circuit, although sometimes it can measure the incorporation of the second term such as when the second term contributes part of the current which the galvanometer measures as motional EMF, e.g. in the Faraday's disk experiment.