When a current-carrying loop is placed in a magnetic field, the loop tends to rotate such that its normal becomes aligned with the magnetic field.

1
When a current-carrying loop is placed in a
magnetic field, the loop tends to rotate such
that its normal becomes aligned with the magnetic
field.
2
The net torque on the loop is given by t IAB
sin f. I is the current in amps, A is the area of
the loop, B is the strength of the magnetic
field, f is the angle between the normal to the
plane of the loop and the direction of the
magnetic field.
3
If the wire is wrapped so as to contain a number
of loops N, the equation becomes t NIAB
sin f.
4
The torque depends on1) the shape and size of
the coil and the current (NIA),2) the magnitude
B of the magnetic field, and3) the orientation
of the normal to the coil to the direction of the
magnetic field (sin f).
5
NIA is known as the magnetic moment of the coil
with the units amperemeter2. The greater the
magnetic moment, the greater the torque
experienced when the coil is placed in a magnetic
field.
6
Ex. 6 - A coil of wire has an area of 2.0 x 10-4
m2, consists of 100 loops, and contains a current
of 0.045 A. The coil is placed in a uniform
magnetic field of magnitude 0.15 T. (a) Determine
the magnetic moment of the coil. (b) Find the
maximum torque that the magnetic field can exert
on the coil.
7
A dc motor is set up in such a way that the
direction of the current produces the proper
torque due to the attraction and repulsion of
permanent magnets. The permanent magnets are
stationary, so the direction of the current must
change to keep the loop rotating.
8
A current-carrying wire can experience a magnetic
force when placed in a magnetic field. A
current-carrying wire also produces a magnetic
field. This phenomenon was discovered by Hans
Christian Oersted.
9
Oersteds discovery linked the movement of
charges to the production of a magnetic field,
and marked the birth of the study of
electromagnetism.
10
When current is passing through a wire the
magnetic field lines are cricles centered on the
wire. The direction of the magnetic field is
found using Right-Hand Rule No. 2 (RHR-2).
11
Right-Hand Rule No. 2 - When the fingers of the
right hand are curled, and the thumb points in
the direction of the current I, the tips of the
fingers point in the direction of the magnetic
field B.
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The strength of the magnetic field is given byB
µ0I/2pr.µ0 is the permeability of free space,
µ0 4p x 10-7 Tm/AI is the current,r is the
radial distance from the wire.
14
Ex. 8 - A long, straight wire carries a current
of I 3.0 A. A particle of charge q0 6.5 x
10-6 C is moving parallel to the wire at a
distance of r 0.050 m the speed of the
particle is v 280 m/s. Determine the magnitude
and direction of the magnetic force exerted on
the moving charge by the current in the wire.
15
Ex. 9 - Two straight wires run parallel. The
wires are separated by a distance of r 0.065 m
and carry currents of I1 15 A and I2 7.0 A.
Find the magnitude and direction of the force
that the magnetic field of wire 1 applies to a
1.5-m length of wire 2 when the currents are (a)
in opposite directions and (b) in the same
direction.
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Ex. 10 - A straight wire carries a current I1 and
a rectangular coil carries a a current I2 . The
wire and the coil lie in the same plane, with the
wire parallel to the long sides of the rectangle.
Is the coil attracted to or repelled from the
wire?
17
At the center of a current-carrying loop of
radius R, the magnetic field is perpendicular to
the plane of the loop and has the value B
µ0I/(2R). If the loop consists of N turns of
wire, the field is N times greater than that of a
single loop.
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At the center of a circular, current-carrying
loop B Nµ0I/(2R). RHR-2 enables us to
find the direction of the magnetic field at the
center of the loop.
19
Ex. 11 - A long, straight wire carries a current
of I1 8.0 A. A circular loop of wire lies
immediately to the right of the straight wire.
The loop has a radius of R 0.030 m and carries
a current of I2 2.0 A. Assuming that the
thickness of the wires is negligible, find the
magnitude and direction of the net magnetic field
at the center C of the loop.
20
A coil of current-carrying wire produces a
magnetic field exactly as if a bar magnet were
present at the center of the loop. Changing the
direction of flow of the current changes the
polarity of the magnetic field. Two adjacent
loops can attract or repel each other depending
on the direction of flow of the current.
21
A solenoid is a long coil of wire. If the coils
are tightly packed and the solenoid is long
compared to its diameter, the magnetic field
inside the solenoid and away from its ends is
nearly constant in magnitude and directed
parallel to the axis.
22
The magnitude of the magnetic field in a solenoid
is B µ0nI. n is the number of turns per unit
length of the solenoid (turns/meter) and I is
the current.
23
If the length of the solenoid is much greater
than its diameter, the magnetic field is nearly
zero outside the solenoid.A solenoid is often
called an electromagnet. They are used in MRIs
cathode ray tubes, power door locks, etc.
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The magnetic fields produced by long straight
wires, wire loops, and solenoids are distinctly
different.
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Although different, each field can be obtained
from a general law Amperes Law.
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Amperes law is valid for a wire of any
shape.For any current geometry that produces a
magnetic field that does not change in time,
?Bll ? l µ0I.
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?Bll ? l µ0I? l is a small segment of length
along a closed path of arbitrary shape around the
current,Bll is the component of the magnetic
field parallel to ? l,I is the net current,?
indicates the sum of all Bll ? l
28
The magnetic field around a bar magnet is due to
the motion of charges, but not the flow of
electricity. It is due to the motion of the
electrons themselves. The orbit of the electron
around the nucleus is like an atom-sized loop of
current, in addition the electron spin also
produces a magnetic field.
29
In most substances, the total effect of all the
electrons cancels out. But in ferromagnetic
materials it does not cancel out for groups of
1016 to 1018 neighboring atoms. Instead some of
the electron spins are naturally aligned forming
a small (0.01 to 0.1 mm) highly magnetized region
called a magnetic domain.
30
Each domain behaves as a small magnet. Common
ferromagnetic materials iron, nickel, cobalt,
chromium dioxide, and alnico.
31
In ferromagnetic materials the domains may be
arranged randomly, so it displays little
magnetism. When placed in an external magnetic
field, the unmagnetized material can receive an
induced magnetism.
32
The domains that are parallel to the field can be
caused to grow by adding electrons to their
domain. Some domains may even reorient to be
aligned with the magnetic field.
33
Induced magnetism causes the previously
nonmagnetic material to behave as a magnet. A
weak field can produce an induced field which is
100 to 1000 times stronger than the external
field.
34
In nonferromagnetic materials, like aluminum and
copper, domains are not formed, so magnetism
cannot be induced.
35
The ampere is now defined as the amount of
electric current in each of two long, parallel
wires that gives rise to a magnetic force per
unit length of 2 x 10-7 N/m on each wire when
the wires are separated by one
meter.(previously I ?q/?t)
36
One coulomb is now similarly defined as the
quantity of electrical charge that passes a given
point in one second when the current is one
ampere, or 1 C 1As.
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