Download 26.2 Magnetic field

 Physics
 Comb. Sci.
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26 Electromagnetism
26.1 Permanent magnets
Learning objectives

Realize the interactions between magnetic poles and their interaction with
magnetic materials.
Key ideas

A magnet has two magnetic poles: the magnetic __________________ (N-pole)
and the magnetic __________________ (S-pole).

When a permanent magnet approaches another magnet, they exert
________________________ on each other.

Unlike magnetic poles __________________ each other; like magnetic poles
__________________ each other.

Magnetic poles always exist in pairs of __________________ polarities. Isolated
magnetic poles do not exist.

When a piece of magnetic material is brought close to the pole of a permanent
magnet, it is __________________ and behaves like a temporary magnet.
1.
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Example 26.1A
 Physics
 Comb. Sci.
Permanent magnets or iron bars? ( p.248)
Bars A, B and C can either be magnets or iron bars. The figures below show the
interaction between bars A and B, and that between bars B and C. State whether they
are iron bars or permanent magnets. Explain briefly.
A
Solution
2.
B
B
C
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26.2 Magnetic field
Learning objectives

Understand the concept of magnetic field and examine the field around a magnet
qualitatively.

Use field lines to represent a magnetic field.
Key ideas

A ______________________ is defined as a region in which a magnet or a
magnetic body experiences a magnetic force.

The SI unit of magnetic field is the _________________ (T).

Magnetic fields can be represented by __________________________:
–
The direction of a field line gives the ______________ of the magnetic field
at a point. For a point where the field line is curved, the direction of the field
is indicated by the ________________ of the field line at that point.
–
The density of field lines is proportional to the ______________ of the
magnetic field in a local region.

Magnetic field lines start from _________________________ and end at
_________________________.

Magnetic field lines do not cross one another or branch at any point.

A ___________________ is used for measuring steady magnetic fields. A search
coil is used for measuring time-varying magnetic fields.
3.
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Example 26.2A
 Physics
 Comb. Sci.
Magnetic field pattern of a cylindrical magnet
( p.254)
Cylindrical magnets can be found in moving-coil microphones. Sketch the magnetic
field pattern of the magnet.
Solution
S
N
4.
 Physics
 Comb. Sci.
26.3
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Magnetic fields due to electric currents
Learning objectives

Realize the existence of magnetic fields due to currents.

Examine the magnetic field patterns associated with current-carrying long straight
wires, circular coils and long solenoids qualitatively.

Apply equations of the magnetic fields around a current-carrying long straight
wire and a long solenoid to solve problems.
Key ideas

_____________________ or, more precisely, moving charges set up magnetic
fields around them.

The magnetic field lines around a long current-carrying straight wire are
concentric circles. The direction of the field can be obtained by the
___________________________________.

The magnetic field B at a point with a distance r away from a long straight wire
carrying a current I is given by

The magnetic field lines at the centre of a flat circular coil are straight and
_____________________ to the plane of the coil.
5.
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
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The magnetic field lines outside a current-carrying _____________________ is
similar to those around a bar magnet. The poles of a solenoid can be determined
by the ___________________________________ for solenoids.

For an N-turn solenoid of length l carrying a current I, the magnetic field B at a
point on the axis near the centre of the solenoid is given by

The magnetic field at the ends of the solenoid on the axis drop to ____________
of the value at the centre.
6.
 Physics
 Comb. Sci.
Example 26.3A
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Resultant magnetic field pattern ( p.262)
Sketch the magnetic field lines around two current-carrying wires.
Solution
(a)
(b)
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Example 26.4A
 Physics
 Comb. Sci.
Magnetic field around a wire ( p.265)
A long straight carrying wire is aligned with the Earth’s magnetic field on the ground.
A current of 3 A flows through it from south to north. Find the magnitude and direction
of the magnetic field at 10 cm east from the wire. Neglect the Earth’s magnetic field.
Solution
8.
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 Comb. Sci.
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Example 26.5A
The magnitude of magnetic field between
current-carrying wires ( p.265)
Two parallel long straight wires P and Q are separated by a distance of 10 cm. They
carry the same size of current of 2 A but in opposite directions.
Q
P
10 cm
Find the magnitude of the magnetic field along line PQ at 1 cm, 2.5 cm and 5 cm from
P.
Solution
9.
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Example 26.6A
 Physics
 Comb. Sci.
Resultant magnetic field ( p.269)
A 500-turn solenoid of length 40 cm, carrying a current of 45 mA, is oriented with its
axis pointing northeast. Assume the Earth’s magnetic field around the solenoid is fairly
uniform and has a magnitude of 50 μT.
N
B
500 turns
45 mA
A
(a) What are the poles at the ends A and B of the solenoid?
(b) What is the magnitude and direction of the resultant magnetic field at the
midpoint on the axis of the solenoid?
Solution
(a) _________________________________________________________________
_________________________________________________________________
(b) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
10.
 Physics
 Comb. Sci.
26.4
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Electromagnets
Learning objectives

Know the applications of electromagnets and examine the factors affecting their
strength.
Key ideas

An ____________________ is usually a current-carrying solenoid with a soft iron
core. It can be switched on and off and its magnetic field can be controlled by
varying the direction and the size of the _________________ passing through it.


The magnetic field of an electromagnet can be made stronger by
–
increasing the _________________ through the coil,
–
increasing the _________________________ per unit length of the coil, and
–
inserting a ______________________ into the coil.
Electromagnets are used in
–
electromagnetic cranes,
–
electric bells and buzzers,
–
relays and circuit breakers,
–
earpieces of telephone receivers, and
–
maglev trains.
Follow-up
Checkpoint ( p.275)
Exercise ( p.279)
11.
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26.5
 Physics
 Comb. Sci.
Current-carrying conductor in a magnetic field
Learning objectives

Study the force acting on a current-carrying wire in a magnetic field and represent
the force with an equation.

Define the ampere with the force between currents in long straight parallel wires.
Key ideas

A current-carrying conductor may experience a _____________________ in a
magnetic field.

When a current-carrying straight wire is placed in a uniform magnetic field at
right angles, the relative directions of the force, the field and the current can be
predicted by ____________________________________.

A _____________________ is a set-up that can be used to study the magnetic
force on a current-carrying wire quantitatively.

The magnetic force F acting on a wire segment of length l which carries a current
I and makes an angle θ with an external magnetic field B is given by

Currents in _____________________ direction attract each other, while currents
in __________________ directions repel each other.
12.
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Example 26.7A
Magnetic force ( p.287)
A metal rod PQ of 0.8 m long is put in a magnetic field as shown. When the source is
switched on, a force of 5 N has to be applied to the rod to keep it stationary. The
magnitude of the magnetic field is 1.5 T.
conducting rail
applied force
current source
conducting rail
(a) What is the direction of the current flowing through the rod? Explain briefly.
(b) What is the size of the current?
Solution
(a) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
(b) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
13.
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Example 26.8A
 Physics
 Comb. Sci.
Magnetic force acting on a wire ( p.287)
A uniform magnetic field of 3 T makes an angle of 30 with the horizontal. A wire of
length 15 cm and carries a current of 5 A which flows from Q to P. It is put on the
same plane as the magnetic field. Find the magnitude and direction of the magnetic
force acting on the wire.
5A
30°
Solution
14.
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 Comb. Sci.
Example 26.9A
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Resultant magnetic force due to current-carrying
wires ( p.290)
Each of the wires P, Q and R carries a current of 3 A.
0.05 m
0.1 m
(a) Draw the magnetic forces acting on R by P and Q.
(b) What is the magnitude of the resultant magnetic force per unit length acting on R?
Solution
(a)
0.05 m
0.1 m
(b) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
15.
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26.6 Applications of magnetic forces on currents
Learning objectives

Determine the turning effect on a current-carrying coil in a magnetic field and
know how a d.c. motor and related appliances work.
Key ideas

A magnetic field may produce a turning effect on a current-carrying coil placed in
the field. For an N-turn coil of area A which carries a current I and makes an angle
with a uniform magnetic field B, the corresponding moment is given by

A _________________________________ is a sensitive device used for
measuring small electric currents or voltages. It makes use of the
_________________ on a current-carrying coil in a magnetic field.

A d.c. motor can rotate a coil in one direction continuously with the help of a
____________________ and a pair of _______________ to reverse the current
flowing through the coil in each half-cycle.

A practical motor contains several coils of many turns wound on a soft iron core
at different angles. The coil and core together are called an _______________.
16.
 Physics
 Comb. Sci.
Example 26.10A
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Motor ( p.300)
A simple motor is composed of a coil of 100 turns, two magnets with opposite poles
facing each other and a cell. The length and width of the coil are 3 cm and 2 cm
respectively. The magnitude of the magnetic field between the magnets is 3 T. The
current flowing in the coil is 1.5 A.
(a) What is the moment about the turning axle of the coil when the normal of the coil
makes an angle of
(i) 60,
(ii) 45, and
(iii) 30
with the magnetic field?
(b) What is the advantage of replacing the pair of magnets with another pair
with cylindrical surfaces?
Solution
(a) (i)
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
(ii) _____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
17.
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(iii) _____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
(b) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
18.