Download When a current-carrying loop is placed in a magnetic field

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.
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.
If the wire is wrapped
so as to contain a
number of loops N,
the equation
becomes:
t = NIAB sin f.
The torque depends on:
1) the shape and size of the
coil and the current (NIA),
2) the magnitude B of the
magnetic field, and
3) the orientation of the normal
to the coil to the direction of
the magnetic field (sin f).
NIA is known as the magnetic
moment of the coil with the
2
units ampere•meter .
The greater the magnetic
moment, the greater the
torque experienced when the
coil is placed in a magnetic
field.
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.
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.
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.
Oersted’s discovery linked
the movement of charges
to the production of a
magnetic field, and
marked the birth
of the study of
electromagnetism.
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).
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.
The strength of the magnetic
field is given by:
B = µ0I/2πr.
µ0 is the permeability of free
-7
space, µ0 = 4π x 10 T•m/A
I is the current,
r is the radial distance from
the wire.
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.
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.
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?
At the center of a currentcarrying 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.
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.
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.
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.
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.
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.
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
MRI’s cathode ray tubes, power
door locks, etc.
The magnetic fields
produced by long
straight wires, wire
loops, and solenoids
are distinctly
different.
Although different,
each field can be
obtained from a
general law:
Ampere’s Law.
Ampere’s 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.
∑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
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.
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.
Each domain behaves
as a small magnet.
Common ferromagnetic
materials: iron, nickel,
cobalt, chromium
dioxide, and alnico.
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.
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.
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.
In nonferromagnetic
materials, like
aluminum and copper,
domains are not
formed, so magnetism
cannot be induced.
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)
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 = 1A•s.