Transcript Electromagnetic Waves - Otterbein University

Rank the magnitude of current induced
into a loop by a time-dependent current
in a straight wire.
I(t)
A B C D
t
E
I(t) Iinduced
What is the direction of the induced
current in the loop?
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•
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Zero
counterclockwise
clockwise
Some other
direction
What is the direction of the induced
current in the loop?
•
•
•
•
Zero
counterclockwise
clockwise
Some other
direction
S
N
When the switch is closed, the potential
difference across R is…
V
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•
•
•
N1
Zero
V N2/N1
V N1/N2
V
N2>N1
R
Once the switch is closed, the ammeter
shows…
V
N1
N2>N1
A
R
• Zero Current
• Steady Current
• Nonzero Current for a short time
A transformer is fed the voltage signal Vp(t).
What is the secondary voltage signal?
Vp(t)
t
The concept of self-inductance
resembles …
• Aging; the older you get, the weaker you
get
• Being taxed; the more money you make, the
more taxes you pay
• Swimming; the more you press the water
away, the harder the water presses back
• Baron Muenchausen; he pulled himself out
of the swamps by his own hair
Self-inductance L is analogous to …
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Electric charge
Potential energy
(Inertial) mass
Momentum
(Hint: it has to be a property of an object)
Given are the potential energies U as a
function of the current I of several
inductors. Which has the smallest selfinduction L?
U
U
I
U
I
U
I
I
A Solenoid produces a changing magnetic
field that induces an emf which lights bulbs
A & B. After a short is inserted, …
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A goes out, B brighter
B goes out, A brighter
A goes out, B dimmer
B goes out, A dimmer
A
xxx
xx
B
A straight wire carries a constant current I. The
rectangular loop is pushed towards the straight
wire. The induced current in the loop is …
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Zero
Clockwise
Counter-clockwise
Need more information
I
When the switch is closed in an LR circuit,
the current exponentially reaches the
maximal value I=V/R. The time constant is
τ =L/R. After which time does the current
reach half its maximal value?
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Immediately
After 1 time constant (t = τ)
After 2 time constants (t = 2τ)
After about 70% of a time constant (t = 0.69τ )
When the switch is closed in an LR circuit, the
current exponentially reaches the maximal value
I=V/R. If the inductor (a solenoid, say), is
replaced by a solenoid with twice the number of
windings, the time the current takes to reach half
its maximal value …?
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does not change
is halved
doubles
quadruples
The current in an LC circuit will oscillate with a
frequency f. To change the frequency we can…
• … change the initial charge of the capacitor
• … change the inductance of the inductor
• …do nothing. It is fixed by the physics of LC
circuits.
The current in an LC circuit will oscillate with a
frequency f. If we replace the capacitor by one
with twice its capacitance, the frequency …
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doubles
quadruples
is halved
None of the above.
The current in an LC circuit will oscillate
with a frequency f. If we add a small
resistance to the circuit, …
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the frequency goes up
the amplitude goes down
the current decays exponentially
Two of the above
Assume a sinusoidal current: I=I0sinω t. In
an AC circuit with a resistor R, which
diagram describes the voltage across the
resistor correctly?
V
V
t
V
t
V
t
t
Assume a sinusoidal current: I=I0sinω t. In
an AC circuit with an inductor L, which
diagram describes the voltage across the
inductor correctly?
V
V
t
V
t
V
t
t
Assume a sinusoidal current: I=I0sinω t. In
an AC circuit with an capacitor C, which
diagram describes the voltage across the
capacitor correctly?
V
V
t
V
t
V
t
t
Resistor
Inductor
• Potential difference
(voltage) gets
current flowing
• Induction slows
current down
Voltage first!
Capacitor
• Flow of charges
(current) builds
up electric field
(voltage)
Current first!
LRC circuit with AC driving emf
• Voltages different: VR , VL , VC
• Common to all: current
 Use current as reference
Phasors
• Phasors turn with
angular frequency ω
• Direction is position
within cycle
• Length of phasor is
peak value of V, I, Z
• Value is projection
on y axis
• E.g.: VC=0, VR=VR0
A little later …
• ALL phasors
have turned by an angle ωt
• Angles between phasors are preserved
• ALL values of V, I have changed
• E.g.: VL(t=later) = VL0sin (ωt+π/2)
Projections on x-axis are values at
time t
Adding Phasors
• Add like
vectors
• Phase angle will
be between 90
and -90
Assume a sinusoidal current: I=I0sin(2πf t). In a
resistor circuit with frequency 2 Hz, which
phasor diagram describes the voltage across the
resistor at t = 1.5 s if the phase at t=0 was zero?
Assume a sinusoidal current: I=I0sinω t. In
an AC circuit with a capacitor C, which
phasor diagram describes the voltage across
the capacitor correctly?
Assume a sinusoidal current: I=I0sinω t. In
an AC circuit with a inductor I, which
phasor diagram describes the voltage across
the inductor correctly?
Assume a sinusoidal current: I=I0sin(2πf t).
What can you tell from the phasor diagram
below about an LRC ac circuit if the orange
arrow represents the instantaneous voltage
across the whole circuit?
The frequency is 1/8 Hz
The phase angle of the current
is about 30 degrees
The inductive reactance is smaller
than the capacitive reactance
The resistance is very small
Assume a sinusoidal current: I=I0sin(2πf t).
Which of the following is true about an LRC ac
circuit?
The phase angle between current and voltage
constant
The voltage is constant
The power consumed by the circuit is zero
The power consumed by the circuit is constant
Group Work on AC LRC circuits
• L=200mH, R=1000 Ohm, C = 60μF, driven by a
30V power supply at 1kHz.
• Draw the voltages and the current in a phasor
diagram at t=1/4000 s.
• Calculate the reactances
• Calculate the impedance of the circuit
• Find the phase angle
• What is the (average) power used by the circuit?
In Physlet I 31.7 an RC circuit is animated.
What happens if the frequency increases?
Nothing except the voltage phasor rotating faster
The reactance of the capacitor goes up and hence
the phase angle between voltage and current
changes
All reactances (R, C) change
The reactance of the inductor goes up, of the
capacitor goes down, and the voltage phasor
rotates faster
In Physlet I 31.7 an RC circuit is animated.
What will happen if the frequency is
halved?
The reactance of the resistor halves
The reactance of the capacitor doubles
The peak voltage across the source changes
The phase angle between the voltage across
R and the voltage across C changes
In Physlet I 31.7 an RC circuit is animated.
What will happen if the frequency is
halved?
The voltage across the resistor halves
The voltage across the capacitor doubles
The peak voltage across the source changes
None of the above
Why does the voltage across the capacitor
not double if the frequency is halved?
The reactance of the capacitor does not
double
The current through the circuit drops
The peak voltage across the source
does not change
The phase angle between the voltages does
not change enough
Consider a LRC circuit which at f =
1kHz displays R=XC=XL=1000Ω.
At 10 kHz we have …
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R=XC=XL=1000Ω
R=1000Ω, XC > XL=10000Ω
R = XC = XL=10000Ω
R=1000Ω, XC =100Ω < XL
Consider a LRC circuit which at f =
1kHz displays R=XC=XL=1000Ω.
At 10 Hz we have …
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R=XC=XL=1Ω
R=1000Ω, XC > XL=1Ω
R = XC = XL=1MΩ
R=1000Ω, XC =100Ω < XL
In Physlet I 31.8 the impedance Z of
a LRC circuit is plotted. What
happens if the value for R is chosen
very big?
• Plot changes, but remains qualitatively the
same
• Nothing changes
• The curve is shifted up
• The curve becomes flat
The impedance of a LRC circuit
depends on the frequency. What is
special about the frequency where
capacitor and the inductor have the
same reactance?
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Nothing
Impedance has a minimum
Current is at a minimum
All voltages are in phase
As one of Maxwell’s equations,
Gauss’s Law is …
• Homogeneous and concerning the electric
field
• Inhomogeneous and concerning the electric
field
• Homogeneous and concerning the magnetic
field
• Inhomogeneous and concerning the
magnetic field
As one of Maxwell’s equations,
(modified) Ampere’s Law is …
• Homogeneous and concerning the electric
field
• Inhomogeneous and concerning the electric
field
• Homogeneous and concerning the magnetic
field
• Inhomogeneous and concerning the
magnetic field
As one of Maxwell’s equations,
magnetic Gauss’s Law is …
• Homogeneous and concerning the electric
field
• Inhomogeneous and concerning the electric
field
• Homogeneous and concerning the magnetic
field
• Inhomogeneous and concerning the
magnetic field
As one of Maxwell’s equations,
Faraday’s Law is …
• Homogeneous and concerning the electric
field
• Inhomogeneous and concerning the electric
field
• Homogeneous and concerning the magnetic
field
• Inhomogeneous and concerning the
magnetic field
Electromagnetic Waves
• Medium = electric and magnetic field
• Speed = 3 105 km/sec
Production of EM
waves
• Current flowing creates
B field
• Charges accumulating
create E field
EM Waves
radiating out
• As the direction of the
current changes, the
“second half” of the
wave is created
 E, B in opposite
direction as in first half,
but in same direction as
in “back part” of first
half
Wave travels in empty space
Directions of E, B are perpendicular
but in phase
• E, B are perpendicular to direction of
motion of wave  transverse wave
The EM spectrum
Receiving an EM Wave