Chapter 21
Magnetic Induction
Inductance
 [A] When the switch is closed, a sudden change in current occurs in the coil
 [B] This current (from the battery) produces a magnetic field in the solenoid,
which creates an increase (a change) in magnetic flux in the solenoid
 [C] According to Faraday’s law, an emf and current are induced in the coil
 [C] According to Lenz’s law, the induced current flows in a direction such
that its magnetic field (i.e. the induced magnetic field) opposes the
magnetic field in [B], which is due to the current from the battery
Section 21.4
Inductor
 A coil is a type of circuit element called an inductor
 Many inductors are constructed as small solenoids
 Almost any coil or loop will act as an inductor
 Whenever the current through an inductor changes,
a voltage is induced in the inductor that opposes this
change
 This phenomenon is called self-inductance
 The current changing through a coil induces a current
in the same coil
 The induced current opposes the original applied
current, from Lenz’s Law
Section 21.4
Inductance of a Solenoid
 Similarly to “capacitors”, which have a “capacitance”,
“inductors” have an “inductance”
 Faraday’s Law can be used to find the inductance of
a solenoid
 L is the symbol for inductance
ì oN 2 A
L=
l
 The voltage across the solenoid can be expressed in
terms of the inductance
å = "L
!I
!t
Section 21.4
Inductance, final
 The results apply to all coils or loops of wire
 The value of L depends on the physical size and
shape of the circuit element
!I
 The voltage drop across an inductor is VL = L
 The unit of inductance is the Henry
 1H=1V.s/A
!t
Section 21.4
RL Circuit
 DC circuits may contain resistors, inductors, and
capacitors
 The voltage source is a battery or some other source that
provides a constant voltage across its output terminals
 Behavior of DC circuits with inductors
 Immediately after any switch is closed or opened, the
induced emfs keep the current through all inductors equal
to the values they had the instant before the switch was
thrown
 After a switch has been closed or opened for a very long
time, the induced emfs are zero (because the B flux is in a
steady state)
Section 21.5
RL Circuit Example
Section 21.5
RL Circuit Example, Analysis
 The presence of resistors and an inductor make the
circuit an RL circuit
 The current starts at zero since the switch has been
open for a very long time
 At t = 0, the switch is closed, inducing a potential
across the inductor
 Just after t = 0, the current in the second loop is zero
 After the switch has been closed for a long time, the
voltage across the inductor is zero
Section 21.5
Time Constant
for RL Circuit
 The current at time t is
found by
V
!t
I=
1! e ô
R
(
)
 τ is called the time
constant of the circuit
 For a single resistor in
series with a single
inductor, τ = L / R
 The voltage is given by
VL = V e-t/τ
Section 21.5
Real Inductors
 Most practical inductors are constructed by wrapping
a wire coil around a magnetic material
 Filling a coil with magnetic material greatly increases
the magnetic flux through the coil and therefore
increases the induced emf
 The presence of magnetic material increases the
inductance (similarly capacitors used dielectric
material to increase the capacitance)
 Most inductors contain a magnetic material inside
which produces a larger value of L in a smaller
package
Section 21.5
Energy in an Inductor
 Energy is stored in the magnetic field of an inductor
(for a capacitor the energy is stored in the electric
field)
 The energy stored in an inductor is PEind = ½ L I2
 Very similar in form to the energy stored in the electric
field of a capacitor
 The expression for energy can also be expressed as
PEind
1 ! ì oN 2 A " 2
= #
$I
2% l &
 In terms of the magnetic field,
PEmag
1 2
=
B (volume )
2ì o
Section 21.6
Energy in an Inductor, cont.
 Energy contained in the magnetic field actually exists
anywhere there is a magnetic field, not just in a
solenoid
 Can exist in “empty” space
 The potential energy can also be expressed in terms
of the energy density in the magnetic field
energy density = umag
PEmag
1 2
=
=
B
volume 2 ì o
Section 21.6