Motional emf
(15.4)
(15.5)
(15.3)
Lenz’s Law
(15.1)
Lenz’s law:
the induced emf and the change in flux have opposite algebraic signs.
The induced current in a loop is in the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop.
Lenz’s Law
Induced emf and Electric Fields
We can relate an induced current in a conducting loop to an electric field by claiming that an electric field is created in the conductor as a result of the changing magnetic flux. 
(15.6)
The induced electric field E in Equation 15.6 is a nonconservative field that is generated by a changing magnetic field.
Maxwell’s Equations
(15.7)
(15.8)
(15.9)
(15.10)
Self-Inductance
After the switch is closed, the current produces a magnetic flux through the area enclosed by the loop. As the current increases toward its equilibrium value, this magnetic flux changes in time and induces an emf in the loop.
Self-Inductance
A self-induced emf is always proportional to the time rate of change of the current. 
RL Circuits
Because the inductance of the inductor results in a back emf, an inductor in a circuit opposes changes in the current in that circuit.
A series RL circuit. As the current increases toward its maximum value, an emf that opposes the increasing current is induced in the inductor.
an inductor
RL Circuits
RL Circuits
τ is the time interval required for the current in the circuit to reach (1 – e-1) = 0.632 = 63.2% of its final value ε/R.