Download 28.1 Induced emf and induced current

 Physics
 Comb. Sci.
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28 Electromagnetic induction
28.1 Induced e.m.f. and induced current
Learning objectives

Examine the evidence of induced e.m.f. when a conductor cuts through magnetic
field lines or the magnetic field through a coil changes.

Determine the direction of induced current by Lenz’s law and Fleming’s right
hand rule.
Key ideas

An _______________ is induced whenever a conductor cuts through magnetic
field lines or the magnetic field through a coil changes.


The magnitude of the induced e.m.f. is directly proportional to the rate at which
–
the conductor cuts through the ___________________________, or
–
the _______________ through the coil changes.
The direction of an induced current can be determined by _______________:
An induced current always flows in a direction so as to ________________ the
change producing it.

Lenz’s law is a consequence of the law of conservation of _______________.

_________________________________ can also be used to determine the
direction of an induced current.
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Follow-up
Checkpoint ( p.358)
Checkpoint ( p.365)
Exercise ( p.366)
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Example 28.1A
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Changing magnetic field through a loop ( p.361)
The following shows a metal loop placed in a uniform magnetic field.
(a) What is the direction of the induced current in the loop if the magnitude of the
magnetic field
(i)
decreases, and
(ii) increases?
Explain briefly.
(b) Does the rate at which the magnetic field increases (or decreases) affect the
direction of the induced current?
Solution
(a) (i)
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
(ii) _____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
(b) _________________________________________________________________
_________________________________________________________________
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Example 28.2A
 Physics
 Comb. Sci.
Rotating a loop in a uniform magnetic field
( p.363)
A conducting loop rotates at a constant speed about O in a clockwise direction in a
uniform magnetic field as shown. Explain briefly whether a current flows in the loop
or not.
P
O
Q
Solution
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
4.
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28.2 Faraday’s law and motional e.m.f.
Learning objectives

Define magnetic flux and interpret magnetic field as magnetic flux density.

State the mathematical form of Faraday’s law and apply it to calculate the average
induced e.m.f.

Understand electromagnetic induction involving motion of conductors in
magnetic fields with the concept of motional e.m.f.
Key ideas

The magnetic flux Φthrough a planar surface of area A placed in a uniform
magnetic field B is given by
where is  the angle between the normal of the surface and the field.

___________________ is a scalar quantity with the unit ________________
(Wb). It is a measure of the number of magnetic field lines through a surface.

The magnetic field is sometimes called the ___________________________.

_______________________________________:
The induced e.m.f. in a conductor is directly proportional to the rate of change of
the magnetic flux through the conductor. Mathematically, the average induced
e.m.f. is
The negative sign is another way to state Lenz’s law.
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
 Physics
 Comb. Sci.
For an N-turn coil, if the magnetic flux Φ through each turn is the same, the total
flux through the coil, called the __________________________________,
is ___________.

A _______________________ is the induced e.m.f. arises from the motion of a
conductor in a magnetic field. For a straight conductor of length l at right angles
to a uniform magnetic field B, when it moves at a velocity v perpendicular to its
length and makes an angle with the field, the motional e.m.f. across the ends of
the conductor is given by
Follow-up
Checkpoint ( p.370)
Checkpoint ( p.374)
Checkpoint ( p.377)
Exercise ( p.377)
6.
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Example 28.3A
Magnetic flux through a coil ( p.369)
A uniform magnetic field of 1.5 T rotates around a rectangular coil of width 3 cm and
length 5 cm. What is the flux passing through the coil in each of the following cases?
(a)
(b)
normal
(c)
normal
normal
30°
coil
60°
coil
coil
Solution
(a) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
(b) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
(c) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
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Example 28.4A
 Physics
 Comb. Sci.
Induced current in a wire loop ( p.371)
A square wire loop is put in a magnetic field pointing into the plane. Each side of the
loop is 3 cm long and has a resistance of 1 . The magnetic field changes steadily in
0.01 s. A current of 0.06 mA flows clockwise in the loop.
(a) Is the magnetic field increasing or decreasing?
(b) Find the change in magnitude of the magnetic field.
Solution
(a) _________________________________________________________________
_________________________________________________________________
(b) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
8.
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Example 28.5A
Rotating coil ( p.372)
A coil of 1500 turns rotates clockwise in a uniform magnetic field of 2 T. The coil
completes 4 cycles in a second. The area of the coil is 0.004 m2.
side view
0°
30°
60°
uniform magnetic field
(a) Complete the following table. Calculate the average induced e.m.f. in every 30°
which the coil rotates through. At which angle is the induced e.m.f. maximum?
(b) Describe how the induced e.m.f. changes in the second half of the cycle.
Solution
(a) Applying  = BA cos  and  = −(N)/t
/
0
N / Wb
average  / V
–
30
60
90
120
150
180
–
The induced e.m.f. is maximum when ___________________________________
_________________________________________________________________.
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(b) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
10.
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Example 28.6A
Cutting magnetic field lines ( p.372)
A metal rod is placed at 1 m from O. At t = 0 s, it starts to move uniformly on two
smooth conducting rails with a speed 0.2 m s1. A uniform magnetic field of 2 T is
directed into the plane of the paper. The bulb has a resistance of 1 .
rail
P
0.2 m s−1
O
45°
Q
rail
1m
(a) What is the direction of the induced current when the metal rod starts to move?
(b) (i) Express the change of area ΔA in terms of time t.
(ii) Hence, express the induced e.m.f.  in terms of time t.
(c) When will the power of the bulb exceed 1 W?
Solution
(a) _________________________________________________________________
(b) (i)
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
(ii) _____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
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(c) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
12.
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Example 28.7A
Induced e.m.f. across a rolling metal rod ( p.376)
A metal rod of 0.8 m long slides down an inclined plane from rest in a uniform
magnetic field. The magnitude of the magnetic field is 1.5 T and the plane makes 30
with the horizontal. The acceleration due to gravity g is 9.81 m s−2.
metal rod
30°
side view
(a) Express the velocity of the rod in terms of time t.
(b) Hence, find the induced e.m.f. across the ends of the metal rod in terms of time t.
Solution
(a) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
(b) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
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28.3
 Physics
 Comb. Sci.
Search coil
Learning objectives

Examine changing magnetic fields using a search coil.
Key ideas

A ___________________ can be used to measure a changing magnetic field
quantitatively.

If an N-turn search coil of area A is placed at right angles to a magnetic field that
varies sinusoidally with time, the maximum voltage induced in the search coil is
given by
where f and B0 are the frequency and amplitude of the field respectively.
Follow-up
Checkpoint ( p.381)
14.
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Example 28.8A
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Search coil ( p.380)
A search coil of 1000 turns and with a surface area of 1 cm2 is put in a varying
magnetic field. The following graph is obtained when the plane of the coil is at right
angles to the field.
(a) What is the frequency of the induced e.m.f.?
(b) What is the amplitude of the magnetic field?
Solution
(a) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
(b) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
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28.4
 Physics
 Comb. Sci.
Applications of electromagnetic induction and
generators
Learning objectives

Describe the structure and the working principle of simple d.c. and a.c.
generators.
Key ideas


Electromagnetic induction is used in
–
moving-coil microphones,
–
magnetic storage,
–
electric guitars, and
–
generators.
A __________________ is a device that converts mechanical energy into
electrical energy.

The __________________ in an a.c. generator are used to prevent the twisting of
wires during the rotation of the coil.

The __________________ of a d.c. generator is used to reverse the connection to
the external circuit when the direction of the induced e.m.f. in the coil reverses.

The variation of the induced e.m.f. in a simple a.c. generator and a d.c. generator
are shown below.
A simple _____________ generator
16.
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A simple _____________ generator


The induced e.m.f. of a generator can be increased by
–
_________________ the rotational speed of the coil,
–
using _________________ magnets,
–
winding more turns of wire on the coil,
–
_________________ the area of the coil within the field, and
–
winding the coil on a _________________ core.
For an a.c. generator in a power station, there is an electromagnet, called
_____________, rotating in a set of fixed coils, called the ________________.
Thus, e.m.f. is induced in the stator coils.
Follow-up
Checkpoint ( p.390)
Exercise ( p.391)
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Example 28.9A
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 Comb. Sci.
Output voltage of a simple a.c. generator ( p.388)
The figure below shows how the output voltage of a simple a.c. generator changes with
time.
(a) What is the period of revolution of the coil?
(b) With reference to the graph, when is the coil (i) parallel and (ii) perpendicular to
the magnetic field?
(c) State, if any, the change in the graph if
(i) the coil rotates in the opposite direction,
(ii) the number of turns of the coil is doubled,
(iii) the rotational speed of the coil is doubled.
Solution
(a) _________________________________________________________________
(b) (i)
_____________________________________________________________
(ii) _____________________________________________________________
(c) (i)
_____________________________________________________________
_____________________________________________________________
(ii) _____________________________________________________________
_____________________________________________________________
(iii) _____________________________________________________________
_____________________________________________________________
18.
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28.5
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Eddy currents
Learning objectives

Recognize the occurrence and practical uses of eddy currents.
Key ideas

____________________ are induced currents circulating through a conducting
plate when the plate cuts through magnetic field lines or is placed in a changing
magnetic field.

Two important consequences resulted from eddy currents:
–
_________________________
–
_________________________
Follow-up
Checkpoint ( p.397)
Exercise ( p.398)
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