Magnetic Flux Density
Induction and Inductance
*Property of STI

Magnetic Flux

Conducting Loop in a Magnetic Field

Laws of Induction

Inductance
H0058
1 __________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
• The amount of magnetic flux per unit of
perpendicular area
Magnetic Flux
• Measure of the strength of an electric field
over an area in a field region
*Property of STI
H0058
2 __________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
Magnetic Flux (B)
B = B·A = BAcosθ
A = area
B = magnetic field
• The SI unit of magnetic flux is weber (Wb)
1 Wb = 1 T m2
*Property of STI
H0058
3 __________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
*Property of STI
H0058
4 __________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
B = BAcos0
B = BA
Conducting Loop in a Magnetic Field
B = BAcos90°
B = 0
B = BAcosq
*Property of STI
H0058
5 __________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
*Property of STI
H0058
6 __________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
Induction
• The process of producing current and emf by
changing magnetic field
Induced Current
Faraday’s Law
• States that the induced emf in a closed loop
equals the negative of the time rate of change
of the magnetic flux through the loop
• The current produced by changing magnetic field

Induced EMF
 B
t
• The work done per unit charge in producing induced
current
*Property of STI
H0058
7 __________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
*Property of STI
H0058
8 __________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
Faraday’s Law
• Induced emf appears on the conducting loop
if any of the following happens:
A single loop of wire with an enclosed area of 6.00 ×
10–2 m2 is in a region of uniform magnetic field, with
the field perpendicular to the plane of the loop. The
magnetic field is decreasing at a constant rate of
0.150 T/s. What is the induced emf?
o The magnetic field is changing
o The area of the loop within the magnetic field
is changing
o The conducting loop is rotating while
immersed to magnetic field
*Property of STI
H0058
*Property of STI
9 __________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
B
 0.150 T/s
t
A  6.00 × 10-2 m2
 
 B
BA
B

 A
t
t
t
H0058
10 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
Lenz’s Law
• the induced current runs to the direction in such
a way that it generates a magnetic field to oppose
the changes in the magnetic flux that induced the
current
  (6.00 × 10-2 m2 )(-0.150 T/s)
ε = 9.00 × 10–9 V
*Property of STI
H0058
11 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
*Property of STI
H0058
12 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
A circular conductor was immersed in and out of a
uniform magnetic field as shown in the figure (the
magnetic fields are perpendicular and are pointing
towards this page). Determine whether the current
is clockwise, counterclockwise or none in the
following situations:
a. The conductor is being moved
into the region of magnetic
field.
b. The entire conductor is at rest
within the magnetic field.
a. Counterclockwise
b. No induced current
c. Clockwise
B
i=?
c. The conductor is being pulled
out of the magnetic field.
*Property of STI
H0058
13 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
A rectangular conductor of unknown length and
width of 0.2 m moves at 12 m/s to the right. It is
oriented perpendicular to a magnetic field of 0.4T as
shown in the figure below.
*Property of STI
H0058
14 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
a.
  B
A
( 0.2 m )( x )
 B
t
t
 (0.4 T)(0.2 m)12m/s
  0.96V
a. What is the induced
emf in the circuit?
b.
b. What is the direction of the
induced current?
c. If the resistance across the
loop is 0.3 Ω, what is the
current?
*Property of STI
H0058
15 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
c.
clockwise
i
0.96 V
V 


0 .3 
R R
i = 3.2 A
*Property of STI
H0058
16 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
Inductor
Inductance
• Device used to produce a desired magnetic field
• Characteristic of an electrical circuit that
opposes the starting, stopping, or a change in
the value of current
• Its SI unit is henry (H)
1 H = 1 T m2/A
• Usually solenoid in shape
• Its inductance is measured using the equation
L
*Property of STI
H0058
17 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
A current of 5.0 mA passes through a solenoid
inductor with 400 turns and an inductance of 8.0 mH.
What is the magnetic flux through the coil?
B 
Li (8.0  10 3 H)(5.0  10 3 A)

N
400
N B
i
*Property of STI
L = inductance (H)
N = no. of turns of the solenoid
inductor
 B = magnetic flux through the center
of the inductor (Wb)
i = current through the conductor (A)
H0058
18 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
Self-inductance
• Happens when two adjacent turns of a solenoid
inductor induced one another due to changing
electric current
• The result of this is the intended function of
inductors: to resist changes in current
= 1.0 × 10–7 Wb
*Property of STI
H0058
19 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
*Property of STI
H0058
20 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
Self-inductance
Self-inductance
• The self-induced emf is the emf that arises due to
the turns in the inductor inducing one another
o Self-induced emf opposes the current
• The inductance does not oppose the current itself,
only the change in current; it opposes both increase
and decrease in current
• The self-induced emf can be solved using the
formula:
 L  L
*Property of STI
i
t
H0058
*Property of STI
21 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
The figure shows an emf L induced in a coil. Which
of the following can describe the current through the
coil?
a. constant and rightward
b. constant and leftward
L
c. increasing and rightward
d. increasing and leftward
22 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
Mutual Inductance (M)
• Proportionality between the emf generated in a coil
to the change in current in the other coil which
produces it
• Arises when two coils in close proximity induces emf
to one another
e. decreasing and rightward
f.
H0058
M  M 21  M12
decreasing and leftward
M
Answer: Options (d) or (e)
*Property of STI
H0058
23 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
*Property of STI
N 2  B 21 N1 B12

i1
i2
H0058
24 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
Mutual Inductance (M)
• Notation: the subscript that stands for the inducing
coil comes second and the subscript that stands for
the coil being induced comes first
• Equations of induced emf:
 21  M 21
i 1
t
*Property of STI
 12  M12
i 2
t
H0058
25 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
a.
 12  M12
i 2
t
M  M12   12


1
t

 (25  103 V) 
i 2
 15.0 A/s 
= –1.67 × 10–3 H or –1.67 mH
b.
M
N 2  B 21
i1
 B 21  Mi 1 = (1.67 × 10–3 H)(3.60 A)
= 6.0 × 10–3 Wb or 6.0 mWb
*Property of STI
H0058
27 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
Two single-turn coils are fixed in location such that
they can induce emf to one another.
a. When the first coil has no current and the current
in the second coil increases at rate of 15.0 A/s, the
emf in the first coil is 25.0 mV. What is their
mutual inductance?
b. When the second coil has no current and the first
coil has current of 3.60 A, what is the flux linkage
in the second coil?
*Property of STI
H0058
26 _________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________