Motional Electromorive Force

 Faraday's law of electromagnetic induction was discovered in 1831. Faraday?s law states that induced emf in a circuit is equal to the negative value of the rate of change of magnetic flux through the circuit εind = - ΔΦ/Δt. The magnetic flux through the circuit can change due to two reasons. Reason 1. The magnetic flux changes due to the motion of the circuit in a time-independent magnetic field. This is the case of moving conductors in a magnetic field. The appearance of induced emf is explained by the magnetic force acting on the electrons in the moving conductors. Consider an induced emf in a rectangular circuit in uniform magnetic field B that is perpendicular to the plane of the circuit. Let one of the sides with length L move with velocity v along the other two sides. The magnetic force acts on the free charges in this part of the circuit. One of the components of this force, connected with the velocity v of the conductor, moves alongside the conductor. This component equals FA = qvB. The work of the component on displacement L equals W = FAL = qvBL. By the definition of emf, εind = W/q = vBL. In the stationary parts of the circuit, emf equals zero. The last equation can be rewritten in a more convenient form. During the change in time Δt, the area of the circuit changes by S = -LvΔt. The change of the magnetic flux during this time equals ΔΦ = -BLvΔt. Therefore, εind = - ΔΦ/Δt. If the resistance of the circuit is R, the current will be εind/R. Reason 2. The second reason for changes in the magnetic flux through the circuit is a change of the magnetic field as a function of time, while the circuit itself remains stable. In this case, the appearance of induced emf cannot be explained in terms of magnetic forces. Electrons in a static conductor can only be moved by an electric field that is directly produced by the changes in the magnetic field. Such an electric field is non-electrostatic. The work of a non-electrostatic electric field done on a unit positive charge as it moves around the loop is equal to the induced emf in the stationary conductor. It was the great English physicist Maxwell who introduced the notion of a non-electrostatic electric field produced by a changing magnetic field to Physics.