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Magnets
by
Charity I. Mulig
Uses
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Electric motors
Electric generators
CRTs
Microwave ovens
Loudspeakers
Printers
Disk drives
Nature of
Magnetism
• The first evidence of
the relationship
between electricity
and magnetism was
discovered in England
by Hans Christian
Oersted in 1820. He
found out that a
current-carrying wire
deflects a compass
needle. Similar
experiments were
done in France by
Andre Ampere.
• Michael Faraday (England) and Joseph Henry
(US) discovered that moving a magnet near a
conducting loop causes a current in the loop.
Faraday’s Law
Any change in the
magnetic
environment of a
coil of wire will
cause a voltage
(emf) to be
induced in the
coil.
Vinduced
N
NBA 


t
t
Pp  Ps
I pV p  I sVs
Np
Vp
Is


N s Vs I p
Magnetic
Field
The magnetic field is
due to the
“distortions” in the
electric field caused
by motion. Magnetic
field is the relativistic
by-product of the
electric field.
General Information
• Produced by moving charges.
• Perpendicular to direction of the charge’s velocity.
• The magnetic field direction is tangent to the
magnetic field line.
• The magnetic field decreases with increasing distance
from the charge which produces it.
• The unit for magnetic field is Tesla (1 T = 1N/Am) or
gauss (1 T = 104 gauss)
• The general form is 
F
B
qv sin 
Magnetic Field of a Moving Charge
Where:
• μ0 is the permeability of free
space which is equal to 4π x 10-7
Wb/A-m
• q is the electric charge
• v is the speed of the charge
• r is the perpendicular distance of
the point where the magnetic field
is being determined and the path of
the moving charge
 o qv
B
2
4r
Note: (For positive charges only)
1. Use your right hand.
2. Point your thumb to the
direction of the velocity.
3. Curl your fingers around the
path traversed by the charge.
This is the direction of the
magnetic field.
Magnetic Field of a Straight CurrentCarrying Wire
o I
B
2s
Where:
• I is the current
• s is the perpendicular distance of
the point and the wire
Magnetic Field of a Current-Carrying
Loop
B
 o NI
2r
Where:
• N is the number of loops
• r is the radius of the loop
Magnetic Field inside a Solenoid
B
 o NI
l
Where l is the length of the solenoid.
Sample Problem 1
Q: Find the magnetic field
in air 10mm from a wire
that carries a current of
1A.
Answer:
2 x 10-5 T
Sample Problem 2
Question:
A solenoid 20 cm long and 40mm in diameter
with an air core is wound with a total of
200 turns of wire. The solenoid’s axis is
parallel to the earth’s magnetic field at a
place where the latter is 3 x 10-5 T in
magnitude. What should the current in the
solenoid be for its field to exactly cancel the
earth’s field inside the solenoid.
Note: μo = 4π x 10-7 T-m/A
Answer:
24 mA
Magnetic
Force
• The magnetic force between two magnets is given by
p1 p 2
F
d2
Where p1 and p2 are the magnetic pole strength and d is the
separation distance of the two magnetic poles.
The Right Hand Rule
Magnetic Force On a Moving Charge
 
FB  qv xB
FB  qvB sin 
Magnetic Force On a Moving Charge
Magnetic Force On a Moving Charge
A magnetic bottle. Particles near either end of the region experience a magnetic force
toward the center of the region. This is one way of containing an ionized gas that has a
temperature of the order of 106 K which could vaporize any material container.
Magnetic Force On a Moving Charge
The Van Allen
radiation belts
around the earth.
Near the poles,
charged particles
from these belts
can enter the
atmosphere,
producing the
aurora borealis
(“northern lights”)
and aurora
australis
(“southern
lights”).
Magnetic Force On a Moving Charge
This bubble chamber image
shows the result of a highenergy gamma ray (which does
not leave a track) that collides
with an electron in a hydrogen
atom. This electron flies off to
the right at high speed. Some
of the energy in the collision is
transformed into a second
electron and a positron (a
positively charged electron). A
magnetic field is directed into
the plane of the image, which
makes the positive and
negative particles curve off in
different directions.
Magnetic Force on a
Current-Carrying Element
FB  ILB sin 
Magnetic Force on Parallel
Current-Carrying Wires
Magnetic Force on a
Current-Carrying Loop
Magnetic Force on a
Current-Carrying Loop
Magnetic Force on a
Current-Carrying Loop
The net
force on a
current loop
in a uniform
magnetic
field is zero.
However,
the net
torque is not
in general
equal to
zero.
Magnitude of Torque on a
Current-Carrying Loop
 
  2 F b 2 sin 
  IBa b sin  
  IBA sin 
  NIAB sin 
Sample Problem
Question:
A particle with mass 35g and charge 50 μC is
moving to the right with velocity 50 m/s in a
strong magnetic field of 2.2T pointing into the
board. Calculate the instantaneous
acceleration that it will experience.
Answer:
0.16 m/s2
Sample Problem
Test your
understanding.
The figure at right
shows a uniform
magnetic field B
directed into the
plane of the
paper (shown by
the blue X’s). A
particle with a
negative charge
moves in the
plane. Which of
the three paths 1, 2 or 3 – does
the particle
follow?
Sample Problem
Sample Problem
Sample Problem
Sample Problem
Question:
A long straight wire carries a current of 100A.
(a) What is the force on an electron moving
parallel to the wire, in the opposite direction
to the current, at a speed of 1 x 107 m/s when
it is 10 cm from the wire. (b) What is the
force on the electron under the same
circumstances when it is moving
perpendicularly toward the wire?
Answer:
2.0 x 10-4 T
3.2 x 10-16 N
Test your understanding.
The figure at right shows a
top view of two conducting
rails on which a conducting
bar can slide. A uniform
magnetic field is directed
perpendicular to the plane
of the figure as shown. A
battery is to be connected
to the two rails so that
when the switch is closed,
current will flow through
the bar and cause a
magnetic force to push the
bar to the right. In which
orientation, A or B, should
the battery be placed in the
circuit?
Applications
Velocity Selector
Cathode Ray Tube
Mass
Spectrometer
Loud Speaker
(a) Components of a loudspeaker. (b) The permanent magnet creates a magnetic field that
exerts forces on the current in the voice coil; for current I in the direction shown, the force is to
the right. If the electric current in the voice coil oscillates, the speaker cone attached to the
voice coil oscillates at the same frequency.
Direct Current Motor
Direct Current Motor