8866 H1 Physics – J2/2011
10.Electromagnetism
Electromagnetism
Content
1.
2.
3.
4.
Force on a current carrying conductor
Force on a moving charge
Magnetic fields due to currents
Force between current carrying conductors.
Candidates should be able to:
(a)
show an appreciation that a force might act on a current carrying conductor placed in
a magnetic field.
(b)
recall and solve problems using the equation F = BIL sin θ, with directions as
interpreted by Fleming’s left hand rule.
(c)
define magnetic flux density and the tesla
(d)
show an understanding of how the force on a current carrying conductor can be used
to measure the flux density of a magnetic field using a current balance.
(e)
predict the direction of a force on a charge moving in a magnetic field
(f)
sketch flux patterns due to a long straight wire, a flat circular coil and a long solenoid.
(g)
show an understanding that the field due to a solenoid may be influenced by the
presence of a ferrous core.
(h)
explain the forces between current carrying conductors and predict the direction of the
forces.
References
1.
2.
3.
4.
Robert Hutchings, “Physics 2nd Ed”, Nelson, 2000
Serway/Faughn, “College Physics 6th Ed,”, Thomson, 2003
Loo KW, “ Longman Advanced Level Physics”, Pearson Longman, 2007
2010 J2 H2 Wave Motion Notes by Chua See How ©JJ
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Jurong Junior College /2011 H2 Physics 9646
Electromagnetism
MAGNETIC FIELD
A field of force is a region of space where there is a force acting on an object placed
in that space. An object placed in an ordinary space (like in deep outer space, which is
not a field) would not have any force acting on it.
The concept of a magnetic field is the same as the concept of a gravitational field or an
electric field. They are special spaces where an object placed in them would have a
force acting on that object. Of course, the object must have the appropriate property in
order that forces would act on it.
In a gravitational field, the object needs to have mass.
In an electric field, the object needs to have charge.
In a magnetic field, the object needs to have magnetic properties (i.e. like iron and
steel) or it is a current carrying conductor or a moving charge.
A magnetic field is a region of space where a magnetic material,
or a current carrying conductor or a moving charge experiences
a force when placed in it.
Fields are produced by objects. A gravitational field is produced by a mass; an electric
field is produced by a charge.
Note:
a. A magnetic field is produced by a permanent magnet or a current-carrying
conductor.
b. A magnetic field can be represented by a diagram of field lines, just like a
gravitational or an electric field.
c. Magnetic field is directed from a North pole to a South pole.
Pattern of the magnetic field produced by
a bar magnet using iron filings
Field lines of a bar magnet
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Electromagnetism
Uniform field strength
A uniform field, within which the field strength is the same at all points, could be
represented as parallel lines that are equally spaced as shown above. The uniform field
is stronger if the lines are closer to each other as shown below.
Strong field
Weak field
The direction of a magnetic field at a point in space is along a tangent to the
magnetic field line at that point.
B
ELECTROMAGNETISM
(a) Show an appreciation that a force might act on a current-carrying conductor
placed in a magnetic field.
As mentioned earlier, a gravitational force acts on a mass in a gravitational field; an
electric force acts on a charge in an electric field, and a magnetic force might act on a
current-carrying conductor in a magnetic field.
Why might, and not definitely would act, like the other two fields? Well, the mass in
the gravitational field is a point mass and the charge in the electric field is a point
charge. By this, we mean the objects (mass and charge) have no size (no volume),
just a point.
For a point mass or charge, there is no direction. The direction of force on the object is
determined by the direction of the field.
In the case of a current-carrying conductor, it has a length and the current must flow
in a certain direction. Depending on the direction of the current, as compared to the
direction of the magnetic field concerned, there is no force if these directions are
parallel.
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Electromagnetism
(c) Define magnetic flux density and the tesla.
The
is given by
Force on
an object is
given by
Gravitational
field strength
Electric
field strength
Magnetic
flux density
F
m
F = mg
F
q
F = qE
F
(something )
F = (something )B
g=
E=
B=
Generally, field strength at a point is expressed as
Field strength =
Force
.
(something)
This (something) in a gravitational field is mass; in an electric field, (something) is
charge. In a magnetic field, (something) is ‘current-carrying conductor’.
•
F
.
m
Consequently, the gravitational force F acting on an object of mass m
placed at that point with gravitational field strength g can be expressed as F
= mg.
•
Electric field strength at a point, E, is expressed as E =
•
•
Gravitational field strength at a point, g, is expressed as g =
F
.
q
Consequently, the electric force acting on an object of charge q placed at
that point with electric field strength E can be expressed as F =qE.
The term ‘magnetic field strength’ is not used nowadays. The term used to represent
field strength in a magnetic field is called ‘magnetic flux density’.
The magnetic flux density at a point, B, is expressed (similar to g and E), as
F
B=
.
(something)
In symbols, (something) here is expressed as (IL sin θ).
density, B, is expressed as
B=
Thus, magnetic flux
F
IL sin θ
where, B = magnetic flux density, F = magnetic force acting on the conductor
I = current, L = length of conductor, θ = angle between B and I
Magnetic flux density in a magnetic field is defined as the force per unit length
acting on a conductor carrying a unit current placed at right angles to the field.
The unit of B is tesla (symbol: T, named after Nikolai Tesla).
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Electromagnetism
Definition of tesla:
The magnetic flux density in a magnetic field is one tesla if one newton of force
is acting on one metre of a conductor carrying one ampere placed at right
angles to the field.
i.e.
1T=
1N
(1A)(1m)sin 90o
(b) Recall and solve problems using the equation F = BlLsinθ, with directions as
interpreted by Fleming’s left-hand rule.
From the equation above, the magnetic force acting on a current-carrying conductor
placed at an angle θ to the magnetic field can be expressed as
F = BILsin θ
Hence, Fmax = BIL when θ = 900 (I is perpendicular to B)
F = 0 when θ = 0 (I is parallel to B)
In Fleming’s left-hand rule, the 3 vectors are represented as such:
• the thumb represents F,
• the index finger represents B, and
• the middle finger represents I.
(in the order of FBI).
Note:
A) F is always perpendicular to B and I,
B) B and I are separated by any angle θ.
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Electromagnetism
Example 1: (Ans: D)
A horizontal power cable carries a steady current in an east-to-west direction, i.e. into the
plane of the diagram.
Which arrow shows the direction of the force on the cable caused by the Earth’s magnetic
field, in a region where this field is at 70o to the horizontal?
(e) Predict the direction of the force acting on a charge moving in a magnetic field.
The direction of the force acting on a moving charge also follows Fleming’s left-hand
rule.
Using Fleming’s left-hand rule, the direction of I is equivalent to the flow of positive
charges with velocity v in that direction. Thus, I is replaced by the vector v, which
represents the velocity of positive charges.
For a negative charge with velocity v, the direction of the force is reversed.
Note:
F
(1) F is always perpendicular to B and v,
(2) B and v are separated by any angle θ.
B (3) For a current-carrying conductor, we have,
θ
F = BILsinθ , the force F acting on a
charge Q moving with a velocity v at an
angle θ to the magnetic field of flux
Q
v
density B is given by the equation
F = BQv sin θ
Example 2: (Ans: D)
Hot air from a hair – dryer contains many positively charged ions. The motion of these ions
constitutes an electric current.
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Electromagnetism
The hot air is directed between the poles of a strong magnet, as shown.
The ions are deflected
A) Towards the north pole N
B) Towards the south pole S
C) Downwards
D) Upwards
(d) Show an understanding of how the force on a current-carrying conductor can be
used to measure the flux density of a magnetic field using a current balance.
A current balance is similar to a beam balance. They both use some ‘weights’ for
measurement. In a beam balance, ‘weights’ on one side is balanced by some other
‘weights’ on the other side. In a current balance as shown in E.g. 4, it is balanced by a
force on a current-carrying conductor. Current balances come in different designs.
Example 3:
A small square coil of N turns has sides of length L and is mounted so that it can pivot
freely about a horizontal axis PQ, parallel to one pair of sides of the coil, through its centre
as shown above. The coil is situated between the poles of a magnet which produces a
uniform magnetic field of flux density B. The coil is maintained in a vertical plane by moving
a rider of mass M along a horizontal beam attached to the coil. When a current I flows
through the coil, equilibrium is restored by placing the rider a distance x along the beam
from the coil. Starting from the definition of magnetic flux density, show that B is given by
Mgx
the expression B = 2 .
IL N
Solution:
The circuit can be redrawn in side view as follows:
coil
F
rider
x
Pivot PQ
F
Mg
B
3D view
side view
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Electromagnetism
The flux density B produced by the pair of magnetic poles is directed vertically downwards
from N to S. To show how this current balance can be used to measure this B, let us
consider taking moments about the pivot PQ:
Referring to side view diagram,
Clockwise moments due to the weight of the rider = Mg.x
Anti-clockwise moments must be due to the forces acting on the square coil.
The vertical sides of the coil are parallel to B, so there is no force acting on these vertical
sides. For the horizontal sides of the coil, the force F acting on the top side must be to the
left and the force acting on the bottom side must be to the right (as indicated on the
diagram), such that there would be anti-clockwise moments for balance. The length of
each side is L, and each side has N conductors, so the force may be expressed as F =
BIL.N.
Hence the anti-clockwise moments due to these forces = BILN.L = BIL2N.
Equating the moments for balance: BIL2N = Mgx
Mgx
IL2 N
Note: The above example serves to show how one particular design of a current balance
may be used to measure B, which in turn depends on the magnetic force acting on currentcarrying conductor(s).
Transposing,
B=
(f) Sketch flux pattern due to a long straight wire, a flat circular coil and a long
solenoid.
Right-hand grip rule:
Thumbs : straight direction
Fingers : curved direction
Flux Pattern:
Flux pattern are diagrams formed by field lines.
The 3 flux patterns due to the 3 shapes of conductor (hence current) are as follows:
1.
Flux pattern of a magnetic field due to current in a long straight wire:
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Electromagnetism
Diagram shows the
flux pattern formed by
iron filings on a flat
horizontal platform due
to current in a vertical
straight wire through
the platform.
2.
Diagram shows a vertical
straight wire carrying an
upwards current, the
directions of the circular
magnetic field lines
follows the right-hand
grip rule.
Flux pattern of a magnetic field due to current in a flat circular coil:
Diagram shows the flux pattern
formed by iron filings on a flat
horizontal platform due to current in a
flat circular coil in a vertical plane
through the platform, its bottom half
circle is hidden under the platform.
3.
Diagram shows the magnetic field
lines, whose direction follows the
right-hand grip rule. The dash lines
show the corresponding positions
between these diagrams.
Flux pattern of a magnetic field due to current in a long solenoid:
Diagram shows the flux pattern formed
by iron filings on a flat horizontal
platform due to current in a long
solenoid; here only the top turns of wire
are shown, the bottom turns are hidden
under the platform.
Diagram shows the magnetic field
lines, whose direction follows the righthand grip rule.
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Electromagnetism
In summary,
Shape of
conductor
(1) Straight wire
Current direction
(I)
Straight (thumb)
Field direction (B)
Curved (fingers)
(2) Flat circular coil
Curved (fingers)
Straight (thumb)
(3) Long solenoid
Curved (fingers)
Straight (thumb)
Remarks on field
direction
Changes, depends
on position
Straight only along
axis of coil
Straight
within
solenoid
(g) Show an understanding that the field due to a solenoid may be influenced by the
presence of a ferrous core.
Ferrous core means the material filling the interior of the solenoid is iron.
The magnetic field due to a solenoid would be stronger when it has a ferrous core, i.e.
the magnetic flux density in the region near that solenoid would be increased, due to the
presence of the ferrous core.
The
due to a
gravitational
field strength
point mass M
electric
field strength
point charge Q
at a point
distance r from M
distance r from Q
is expressed as
g=
GM
r2
E=
Q
4πεo r 2
magnetic
flux density
(1) long straight wire
(2) flat circular coil
(3) long solenoid
carrying a current
I
(1) distance d from I
(2) distance r from I,
i.e. at centre of
coil
(3) within solenoid
μI
(1) B = o
2πd
μ NI
(2) B = o
2r
μo NI
= μo nI
(3) B =
A
Remarks:
The 3 equations for B need not be recalled or derived (will be provided if required in
question).
N is the number of turns in coil or solenoid.
n is number of turns per unit length of the long solenoid.
μo is the permeability of vacuum. If there is a ferrous core, its permeability μ would be
larger than that of vacuum, hence flux density is increased.
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Electromagnetism
Example 4: (Ans: A)
A plotting compass is placed near a solenoid. When there is no current in the solenoid, the
compass needle points due north as shown.
When there is a current from X to Y, the magnetic field of the solenoid at the compass is
equal in magnitude to the Earth’s magnetic field at that point. In which direction does the
plotting compass set?
A
C
B
D
Example 5: (Ans: B)
The diagram shows a flat surface with lines OX and OY at right angles to each other.
Which current in a straight conductor will produce a magnetic field at O in the direction OX?
A
B
C
D
At P into the plane of the diagram
At P out of the plane of the diagram
At Q into the plane of the diagram
At Q out of the plane of the diagram
(h) Explain the forces between current-carrying conductors and predict the direction
of the forces.
In a gravitational field, forces between 2 point masses are always attractive.
In an electric field, forces between 2 point charges are as follows: like charges repel,
unlike charges attract.
In a magnetic field, we consider forces between 2 current-carrying conductors which
are parallel and very thin:
• If the currents are in the same direction, they attract,
• If the currents are in opposite directions, they repel.
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Comparison between the 3 fields:
Field
gravitational
name for strength
field strength
due to a
is expressed as
force on a
point mass M
g=
magnetic
flux density
point charge Q
long straight wire
carrying a current I
μI
B= o
2πd
E=
Q
4πεo r 2
point charge q
= mg
= qE
conductor with
current I, of length
A at angle θ to
direction of field
= BI A sin θ
masses m1, m2
charges Q1, Q2
currents I1, I2
r
r
d
separated by
is expressed as F
electric
field strength
point mass m
is expressed as F
force between 2
GM
r2
Electromagnetism
=
Gm1m2
r2
=
Q1Q2
4πεo r 2
=
μo I1I2
A
2πd
Note for the last row:
• Forces on very long conductors are very large.
• It is more sensible to consider the force on a unit length of a conductor.
F μoI1I2
=
• Force per unit length on a conductor,
.
A 2πd
• θ = 90o ⇒ sin θ = 1, so equation above does not have sin θ (explained later).
Force acting on masses, charges and current-carrying conductors:
For a gravitational force on a mass m2 in a field due to m1,
Gm
Gm1m2
F = m2 (g) = m2 ( 2 1 ) =
r
r2
For an electric force on a charge Q2 in a field due to Q1,
Q1
Q1Q2
F = Q2 (E) = Q2 (
)=
2
4πεo r
4πεo r 2
For a magnetic force on a conductor with current I2 in a field due to another parallel
conductor with current I1, the force per unit length,
μI
μ II
F
= I2 (B) = I2 ( o 1 ) = = o 1 2
2πd
2πd
A
Here, the direction between the B due to I1 and the current I2 are perpendicular, so sin
θ = 1.
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Electromagnetism
To show the direction of the force, when the 2 currents are in the same direction:
B1
I1
•
•
F
I2
In the region on the right of I1, the direction of B1 due to I1 is into the paper
(represented by x x).
In this region B1, the direction of the force F acting on I2, by Fleming’s lefthand rule, is to the left, i.e. towards I1. Hence, the force between 2
parallel conductors with currents in the same direction is attractive.
If the direction of I2 is reversed, the direction of the force F acting on it would also be
reversed (to the right), i.e. repelled by I1.
B1
I1
I2
F
If the direction of I1 is reversed, the direction of the field B1 due to I1 would also be
reversed (out of paper, represented by • •), so the force F acting on I2 in this reversed
field would also be reversed (to the right), i.e. repelled by I1. Hence, the force between
2 parallel conductors with currents in opposite directions is repulsive.
B1
I1
I2
F
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Electromagnetism
Example 6: (Ans: C)
Two long, parallel wires X and Y carry currents of 3 A and 5 A respectively. The force per
unit length experienced by X is 5 x 10-5 N to the right as shown in the diagram (Fig. 18)
The force per unit length experienced by wire Y is
A
B
C
D
2 x 10-5 N to the left
3 x 10-5 N to the right
5 x 10-5 N to the left
5 x 10-5 N to the right
Example 7: (Ans: C)
Two long, straight, parallel wires carry currents of 1.0 A and 2.0 A.
Which diagram shows the directions and relative magnitudes F1 and F2 of the forces per
unit length on each of the wires?
A
C
D
B
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Electromagnetism
Some interesting applications of magnetism and electromagnetism
Magnetic Healthcare
Magnets have always been used to promote health.
Cleopatra wore jewellery charged with magnetism and
Queen Elizabeth 1 is said to have used magnets to ease
her arthritis.
And it hasn't gone out of fashion. People who practice
magnetic theraphy claim that is natural and simple way of
making you feel better is quicker. They say it works on
colds and flu, stress, arthritis and rheumatism, headaches,
muscle strain, period pain and several chronic skin
diseases.
Research has shown that magnetism can make capillary
walls relax and blood vessels widen, allowing more blood
to pass through. This means the body can get rid of toxins
faster and so speed up the healing process.
Electronic Devices
Motors and generators are devices that use electromagnetic induction. Electromagnetic
fields are created by electromagnetic induction which states that moving electrical current
creates an electronic field. Motors and appliances use electric current in order to create an
electromagnetic field to operate the device.
Relays
Relays are how devices such as telephones and computers work. Relays use
electromagnets to control the logic and memory function of these devices.
Generators
Electromagnetic fields that move create electrical current. Generators operate off of this
principle in order to function and create electrical power for homes. Outside power sources
must be used to power the generator in order for the device to create energy.
Transportation
Some trains use electromagnets to
elevate the train cars in order for the
modern locomotive to move at incredible
rapid speeds.
End of lecture notes
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