Transcript When a coil of wire and a bar magnet are moved in relation to each

When a coil of wire and a bar
magnet are moved in relation
to each other, an electric
current is produced. This
current is produced because
the strength of the field at the
location of the coil changes.
This current is an
induced current
and the emf that
produces it is an
induced emf.
An induced emf can also be
produced by changing the
area of a coil in a constant
magnetic field. The rotation
of a coil in a constant
magnetic field also
produces an induced emf.
The current flows because
the coil is a closed circuit. If
it were an open circuit, no
current would flow, so
there would be no induced
current.
There would, however, be
an induced emf.
Producing an
induced emf
with a magnetic
field is called
electromagnetic
induction.
Moving a conducting
rod in a magnetic field
causes opposite
charges to build up on
opposite ends (or
sides) of the rod.
This charge difference
builds up until the
attractive force the
charges have for each
other is equal in
magnitude to the
magnetic force.
The induced emf
produced is called a
motional emf. If the rod
stops moving, the
magnetic force
vanishes, and the
emf disappears.
The electric force on a
positive charge at the end of
the rod is Eq. The electric
field magnitude is given by
voltage difference between
the ends (the emf ε) divided
by the length L.
So, Eq = (ε/L)q. The
magnetic force is F = qvB
(if the charge moves
perpendicular to the field).
These two forces are
balanced, so (ε/L)q = qvB.
emf,
ε = vBL.
Ex. 1 - The rod in the above figure is moving at a
speed of 5.0 m/s in a direction perpendicular to a
0.80-T magnetic field. The rod has a length of 1.6
m and a negligible electrical resistance (like the
rails). The bulb has a resistance of 96 Ω. Find
(a) the emf produced, (b) the induced current,
(c) the electrical power delivered to the bulb,
(d) the energy used by the bulb in 60.0 s.
Motional emf arises because
a magnetic force acts on the
charges in a conductor moving
through a magnetic field. But if
this emf causes a current, a
second magnetic force arises
because the current I in the
conductor is perpendicular to
the magnetic field.
The current-carrying material
experiences a magnetic force
(F = ILB sin90°) that is
opposite the velocity of the
material. This force, by itself,
would slow the rod until it
stopped, which would also
stop the current.
To keep the rod moving,
a force must be added to
balance this opposing
force. This added force
supplies the energy to
produce the electrical
energy of the current in
the conducting material.
Ex. 2 - An external agent supplies a
0.086-N force that keeps the rod
moving at a constant speed of
5.0 m/s. Determine the work done
in 60.0 s by the external agent.
This opposing force to the
motion of the conducting
material through a
magnetic field is one
consequence of the law of
conservation of energy.
Ex. 3 - A conducting rod is free to slide
down (frictionlessly) between two
vertical copper tracks. A constant
magnetic field B is directed
perpendicular to the motion of the rod.
The only force acting on the rod is its
weight. Suppose a resistance R is
connected between the tops of the
tracks. (a) Does the rod now fall with the
acceleration due to gravity?
(b) How does energy conservation apply
to what happens?
A conductor moving across a
magnetic field crosses an area A.
The product of the field strength B
and the area A, BA is called the
magnetic flux: BA = F.
The magnitude of the induced
emf is the change in magnetic flux
∆F = F - F0 divided by the time
interval ∆t = t - t0 during which the
change occurs. ε = ∆F/∆t.
This is almost always
written with a minus sign:
ε = -∆F/∆t as a reminder
that the polarity of the
induced emf is such that it
produces a force opposing
the direction of motion.
This formula,
ε = -∆F/∆t, can
be applied to all
possible ways of
generating induced
emfs.
If the direction of the
magnetic field is not
perpendicular to the surface
swept out by the moving
conductor, we use the
following general equation to
calculate magnetic flux:
ε = -∆F/∆t cos f.
The unit of
magnetic flux is the
2
2
tesla•meter (T•m ).
This unit is called a
weber (Wb).
Ex. 4 - A rectangular coil of
wire is situated in a constant
magnetic field whose
magnitude is 0.50 T. The
coil has an area of 2.0 m2.
Determine the magnetic flux
for the three orientations,
f = 0°, 60.0°, and 90.0°.
The magnetic flux F is
proportional to the number
of field lines that passes
through a surface. Thus, one
often encounters phrases
like. “the flux that passes
through a surface bounded
by a loop of wire.”
The fact that a change of flux
through a loop of wire produces
an emf was discovered by
Joseph Henry (USA) and
Michael Faraday (English). The
key word here is “change.”
Without a change in flux, there
is no emf. A flux that is constant
over time creates no emf.
Faraday’s Law of
Electromagnetic Induction:
The average emf ε induced in
a coil of N loops is:
ε = -N ∆F/∆t.
The unit is the volt
(surprise, surprise).
An emf is generated
if the flux changes for
any reason.
Since F = BA cos f,
B, A, or f could
change.
Ex. 5 - A coil of wire consists of 20 turns,
each of which has an area of 1.5 x 10-3 m2.
A magnetic field is perpendicular to the
surface of the loops at all times. At time
t0 = 0, the magnitude of the magnetic field at
the location of the coil is B0 = 0.050 T. At a
later time t = 0.10 s, the magnitude of the
field has increased to B = 0.060 T. (a) Find
the average emf induced in the coil during
this time. (b) What would be the value of the
average induced emf if the magnitude of the
magnetic field decreased from 0.060 T to
0.050 T in 0.10 s?
Ex. 6 - A flat coil of wire has an area of
0.020 m2 and consists of 50 turns. At
t0 = 0 the coil is oriented so the normal
to its surface is parallel to a constant
magnetic field of magnitude 0.18 T.
The coil is then rotated through an
angle of f = 30.0° in a time of 0.10 s.
(a) Determine the average induced
emf. (b) What would be the induced
emf if the coil were returned to its initial
orientation in the same time of 0.10 s?