Transcript File - sdeleonadvancedphysics

NAT Review
S.Y.2014-2015
2.1 Demonstrate Oersted’s discovery.
He found that magnetism was produced
by current – carrying wires.
2.2 Compare the contributions of Faraday and Oersted to
electromagnetic theory
• Oersted: He found that magnetism was produced
by current – carrying wires.
• Faraday: He concluded that an electric current
can be produced by a changing magnetic field.
2.3 Explain electromagnetic induction.
• Two simple experiments
demonstrate that a
current can be
produced by a changing
magnetic field.
• First: consider a loop of
wire connected to a
galvanometer as shown.
• If a magnet is moved toward the loop, the
galvanometer needle will deflect in one direction.
• If a magnet is moved away from the loop, the
galvanometer needle will deflect in the opposite
direction.
• If the magnet is held stationary relative to the loop, no
galvanometer needle deflection is observed.
• The phenomenon of inducing voltage by
changing magnetic field in a coil of wire is
called electromagnetic induction.
• If the magnet is held stationary and the coil is moved
toward or away from the magnet, the galvanometer
needle will also deflect.
• From these observations, you can conclude that a
current is set up in the circuit as long as there is
relative motion between the magnet and the coil.
• This current is set up in the circuit even though there
are no batteries in the circuit.
• The current is said to be an induced current, which is
produced by an induced EMF.
Faraday’s Experiment
• A coil is connected
to a switch and a
battery.
• This is called the
primary coil and the
circuit is called the
primary circuit.
• The coil is wrapped
around an iron ring
to intensify the
magnetic field
produced by the
current through the
coil.
Faraday’s Experiment
• A second coil, on the
right, is wrapped
around the iron ring
and is connected to a
galvanometer.
• This is secondary coil
and the circuit is the
secondary circuit.
• There is no battery in
the secondary circuit
and the secondary
circuit is not
connected to the
primary coil.
Faraday’s Experiment
• The only purpose of
this circuit is to
detect any current
that might be
produced by a
change in the
magnetic field.
• When the switch in
the primary circuit is
closed, the
galvanometer in the
secondary circuit
deflects in one
direction and then
returns to zero.
Faraday’s Experiment
• When the switch is
opened, the
galvanometer
deflects in the
opposite direction
and again returns to
zero.
• The galvanometer
reads zero when
there is a steady
current in the
primary circuit.
• Faraday concluded that an electric current can be
produced by a changing magnetic field.
• A current cannot be produced by a steady magnetic
field.
• The current that is produced in the secondary circuit
occurs for only an instant while the magnetic field
through the secondary coil is changing.
• An induced EMF is produced in the secondary circuit
by the changing magnetic field.
• In both experiments, an EMF is induced in a circuit
when the magnetic flux through the circuit changes
with time.
• Faraday’s Law of Induction: The EMF induced in a
circuit is directly proportional to the time rate of
change of magnetic flux through the circuit.
EMF  
dΦ
dt the circuit.
– where Φ is the magnetic flux threading
– Magnetic flux Φm :
Φ m   B  dA
• The negative sign is a consequence of Lenz’s law and is
discussed later (the induced emf opposes the change in
the magnetic flux in the circuit).
• If the circuit is a coil consisting of N loops all of the
same area and if the flux threads all loops, the induced
EMF is:
dΦ
EMF   N 
dt
Application of Faraday’s Law
• A coil is wrapped with 200 turns of wire on the
perimeter of a square frame of sides 18 cm. Each turn
has the same area, equal to that of the frame, and the
total resistance of the coil is 2 . A uniform magnetic
field is turned on perpendicular to the plane of the
coil. If the field changes linearly from 0 to 0.5 Wb/m2
in a time of 0.8 s, find the magnitude of the induced
EMF in the coil while the field is changing.
Sol. Loop area = (0.18 m)2 = 0.0324 m2
At t = 0 s, the magnetic flux through the loop is 0
since B = 0 T.
Application of Faraday’s Law
– At t = 8 s, the magnetic flux through the loop is
– Φm = B·A = 0.5 Wb/m2·0.0324 m2 = 0.0162 Wb.
– The magnitude of the induced EMF is:
EMF   N
dΦ

dt
200  0.0162 Wb  0 Wb 
0.8 s  0 s
EMF  4.05 V
Solve:
1. A coil with 25 turns of wire is wrapped on a frame
with a square cross section 1.80 cm on a side. Each
turn has the same area, equal to that of the frame,
and the total resistance of the coil is 0.350 Ὡ. An
applied uniform magnetic field is perpendicular to
the plane of the coil. (a) If the field changes
uniformly from 0.00 T to 0.500 T in 0.800 s, find the
induced emf in the coil while the field is changing.
Find (b) the magnitude and (c) the direction of the
induced current in the coil while the field is
changing.
2. Suppose the magnetic field changes uniformly
from 0.500 T to 0.200 T in the next 0.600 s.
Compute (a) the induced emf in the coil and
(b) the magnitude of induced current.