Lecture 10/3 Chapter 23 Flashcards
Quick Quiz
A square coil, enclosing an area with sides 2.0 cm
long, is wrapped with 2 500 turns of wire. A uniform
magnetic field perpendicular to its plane is turned on
and increases to 0.25 T during an interval of 1.0 s.
What average voltage is induced in the coil?
a. 0 V
b. 0.25 V
c. 0.12 V
d. 2.0 V
b. 0.25 V
Magnetic flux is self changed in first
In second magntic field stayed the same but Flux changed due tot he turning of the coil.
Application of Faraday’s
Law – Motional emf
o A straight conductor of length ℓ moves perpendicularly
with constant velocity through a uniform field
o The electrons in the conductor experience a magnetic
force
o F = q v B
o The electrons tend to move to the lower end of the
conductor
o As the negative charges accumulate at the base, a net positive charge exists at
the upper end of the conductor
o As a result of this charge separation, an electric field is produced in the conductor
o Charges build up at the ends of the conductor until the downward magnetic force
is balanced by the upward electric force
o There is a potential difference between the upper and lower ends of the conductor
ΔV = B ℓ v
A potential difference is maintained across the conductor as long as there is motion through the
field
o If the motion is reversed, the polarity of the potential difference is also reversed
Quick Quiz
An airplane with a wingspan of 60.0 m flies parallel to
the Earth’s surface at a point where the downward
component of the Earth’s magnetic field is 0.400 × l0−4 T.
If the induced potential between wingtips is 0.900 V, what
is the plane’s speed?
a. 250 m/s
b. 338 m/s
c. 375 m/s
d. 417 m/s
c. 375 m/s
*rough answer is ~ 380
Alternating Current (AC) generator
o Converts mechanical energy to electrical energy
o Consists of a wire loop rotated by some external means
o There are a variety of sources that can supply the energy to rotate the
loop
o These may include falling water, heat by burning coal to produce
steam
Basic operation of the generator AC generator
o As the loop rotates, the magnetic flux
through it changes with time
o This induces an emf and a current in the
external circuit
o The ends of the loop are connected to slip
rings that rotate with the loop
o Connections to the external circuit are made
by stationary brushes in contact with the
slip rings
AC Generators – Detail of
Rotating Loop
o The magnetic force on the charges in the
wires AB and CD is perpendicular to the
length of the wires
o An emf is generated in wires BC and AD
o The emf produced in each of these wires
is ε= B ℓ v⊥= B ℓ v sin θ
o The emf generated by the rotating loop can
be found by
o ε =2 B ℓ v⊥=2 B ℓ v sin θ
o If the loop rotates with a constant angular
speed, ω, and N turns
o ε = N B A ω sin ω t
o ε = εmax when loop is parallel to the field
o ε = 0 when when the loop is perpendicular
to the field
Quick Quiz
Considerable scientific work is currently underway to
determine whether weak oscillating magnetic fields such as
those found near outdoor electric power lines can effect human
health. One study indicated that a magnetic field of magnitude
1.0 × 10−3 T, oscillating at 60 Hz, might stimulate red blood cells
to become cancerous. If the diameter of a red blood cell is 8.0
μm, determine the maximum emf that can be generated around
the perimeter of the cell.
a. 0 V
b. 0.019 nV
c. 0.080 nV
d. 1.190 nV
b. 0.019 nV
Transformers
An AC transformer consists of two coils of wire
wound around a core of soft iron
o The side connected to the input AC voltage
source is called the primary and has N1 turns
o The other side, called the secondary, is
connected to a resistor and has N2 turns
o The core is used to increase the magnetic flux
and to provide a medium for the flux to pass
from one coil to the other
o The rate of change of the flux is the same for
both coils
o The voltages are related by
o When N2 > N1, the transformer is referred to as a step up
transformer
o When N2 < N1, the transformer is referred to as a step down
transformer
Transformers Change in Voltage Equation
∆V2=(N2/N1)∆V1
Transformer, final
o The power input into the primary equals the power output at the
secondary
o I1ΔV1 = I2ΔV2
o You don’t get something for nothing
o This assumes an ideal transformer
o In real transformers, power efficiencies typically range from
90% to 99%
Electrical Power Transmission
o When transmitting electric power over long distances, it is most
economical to use high voltage and low current
o Minimizes I2R power losses
o In practice, voltage is stepped up to about 230 000 V at the
generating station and stepped down to 20 000 V at the distribution
station and finally to 120 V at the customer’s utility pole
Quick Quiz
A transformer consists of a 500-turn primary
coil and a 2 000-turn secondary coil. If the
current in the secondary is 3.00 A, what is the
primary current?
a. 0.750 A
b. 1.33 A
c. 12.0 A
d. 48.0 A
c. 12.0 A
There is always loss of power
Self-Inductance
o Self-inductance occurs
when the changing flux
through a circuit arises
from the circuit itself
o The self-induced emf must be proportional to the time rate of
change of the current
o L is a proportionality constant called the inductance of the
device
o The negative sign indicates that a changing current induces an
emf in opposition to that change
Self-Inductance Equation
ε= −L(∆I/∆t)
L is self inductance of the wire
The SI unit of self-inductance is the
Henry
1 H = 1 (V · s) / A
