Summary of Chapter 20 – Induced Voltage and Inductance
Please read Chapter 20 carefully, and make sure that you
understand the summary points below.
►The magnetic flux, Φ, through a planar surface is defined as
θ
cosBA=Φ
where B is the strength of the uniform magnetic field, A is the
cross-sectional area of the surface, and θ is the angle between
B and the direction perpendicular to the plane.
►Faraday's law of induction states that the instantaneous
emf induced in a circuit equals the rate of change of magnetic
flux through the circuit:
tΔ
ΔΦ
−=emf
where Φ is the flux through the surface enclosed by the circuit.
►Lenz's law states that the polarity of the induced emf is such
that it produces a current whose magnetic field opposes the
change in magnetic flux through the circuit.
►If a conducting bar of length C moves through a magnetic
field with a speed, v, so that B is perpendicular to the bar, the
emf induced in the bar, often called a motional emf, is
BLv=em
f
►When a coil of wire with N turns, each of area A, rotates
with constant angular speed ω in a uniform magnetic field B,
the emf induced in the coil is
tNAB
ω
ω
sinem
f
=
►When the current in a coil changes with time, an emf is
induced in the coil according to Faraday's law. This self-
induced emf is defined by the expression
t
I
L
Δ
Δ
−=emf
where L is the inductance of the coil. The SI unit for
inductance is the henry; 1 H=1Vs/A.
►The inductance of a coil can be found from the expression
I
N
LΦ
=
where N is the number of turns on the coil, I is the current in
the coil, and Φ is the magnetic flux through the coil produced
by that current.
►RL circuit. If a resistor and inductor are connected in series
to a battery and a switch is closed at t = 0, the current in the
circuit does not rise instantly to its maximum value. After one
time constant, τ = L/R, the current in the circuit is 63% of its
final value, emf/R.
►The energy stored in the magnetic field of an inductor
carrying current I is
2
2
1LI
L
U=
