Transcript PRS_W15D2

Concept Questions with
Answers
8.02
W15D2
P36 -
W15D2
Final Exam Review
P36 - 2
Concept Question: LC Circuit
Consider the LC circuit at
right. At the time shown the
current has its maximum
value. At this time:
1. the charge on the capacitor has its maximum value.
2. the magnetic field is zero.
3. the electric field has its maximum value.
4. the charge on the capacitor is zero.
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Concept Q. Answer: LC Circuit
Answer: 4. The current is
maximum when the charge on
the capacitor is zero
Current and charge are exactly 90 degrees out of
phase in an ideal LC circuit (no resistance), so when
the current is maximum the charge must be
identically zero.
P36 - 4
Concept Question: LC Circuit
In the LC circuit at right the
current is in the direction
shown and the charges on the
capacitor have the signs
shown. At this time,
1.
2.
3.
4.
I is increasing and Q is increasing.
I is increasing and Q is decreasing.
I is decreasing and Q is increasing.
I is decreasing and Q is decreasing.
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Concept Q. Answer: LC Circuit
Answer: 2. I is increasing;
Q is decreasing
With current in the direction shown,
the capacitor is discharging (Q is
decreasing).
But since Q on the right plate is positive, I must be
increasing. The positive charge wants to flow, and the
current will increase until the charge on the capacitor
changes sign. That is, we are in the first quarter period of
the discharge of the capacitor, when Q is decreasing and
positive and I is increasing and positive.
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Concept: RLC Circuit
1.0I0
0.5Q0
0.5I0
0.0Q0
0.0I0
-0.5Q0
-0.5I0
-1.0Q0
1. It will increase.
Current
Charge
Tlag
0
40
80
Current through Capacitor
1.0Q0
Charge on Capacitor
The plot shows the charge on
a capacitor (black curve) and
the current through it (red
curve) after you turn off the
power supply. If you put a
core into the inductor what will
happen to the time TLag?
-1.0I0
120
Time (mS)
2. It will decrease.
3. It will stay the same.
P36 - 7
Concept Answer: RLC Circuit
Answer: 1. TLag will increase
Current
Charge
Tlag
1.0I0
0.5Q0
0.5I0
0.0Q0
0.0I0
-0.5Q0
-0.5I0
-1.0Q0
0
40
80
Current through Capacitor
Putting in a core increases
the inductor’s inductance and
hence decreases the natural
frequency of the circuit.
Lower frequency means
longer period. The phase will
remain at 90º (a quarter
period) so TLag will increase.
Charge on Capacitor
1.0Q0
-1.0I0
120
Time (mS)
P36 - 8
Concept: RLC Circuit
Current
Charge
Tlag
1.0I0
0.5Q0
0.5I0
0.0Q0
0.0I0
-0.5Q0
-0.5I0
-1.0Q0
0
40
80
Current through Capacitor
If you increase the resistance
in the circuit what will happen
to rate of decay of the
pictured amplitudes?
Charge on Capacitor
1.0Q0
-1.0I0
120
Time (mS)
1. It will increase (decay more rapidly).
2. It will decrease (decay less rapidly).
3. It will stay the same.
P36 - 9
Concept Answer: RLC Circuit
Current
Charge
Tlag
1.0I0
0.5Q0
0.5I0
0.0Q0
0.0I0
-0.5Q0
-0.5I0
-1.0Q0
0
40
80
Current through Capacitor
Answer: 1. It will increase
(decay more rapidly)
Charge on Capacitor
1.0Q0
-1.0I0
120
Time (mS)
Resistance is what dissipates power in the circuit and causes
the amplitude of oscillations to decrease. Increasing the
resistance makes the energy (and hence amplitude) decay
more rapidly.
P36 - 10
Concept Question: Direction of
Propagation
The figure shows the E
(yellow) and B (blue)
fields of a plane wave.
This wave is
propagating in the
1. +x direction
2. –x direction
3. +z direction
4. –z direction
P36 - 11
Concept Question Answer:
Propagation
Answer: 4. The wave is moving in the –z direction
The propagation
directionris given
by
r
the dir E  B
(Yellow x Blue)
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Concept Question: Traveling Wave
r
The B field of a plane EM wave is B( y,t)  B0 sin(ky  t)kφ
The electric field of this wave is given by
1.
2.
3.
4.
r
E( y,t)  E0 sin(ky  t)φ
j
r
E( y,t)  E0 sin(ky  t)(φ
j)
r
E( y,t)  E0 sin(ky  t)φ
i
r
E( y,t)  E0 sin(ky  t)(φ
i)
P36 - 13
Concept Q. Ans.: Traveling Wave
r
Answer: 4. E( y,t)  E0 sin(ky  t)(φ
i)
From the argument of the sin(ky   t) , we know the
wave propagates in the positive y-direction.
So we have Ê ´ B̂ = ?´ k̂ = ĵ Þ Ê = - î
P36 - 14
Concept Question EM Wave
The electric field of a plane wave is:
r
E(z,t)  E0 sin(kz  t)φ
j
The magnetic field of this wave is given by:
1.
2.
3.
4.
r
B(z,t)  B0 sin(kz  t)φ
i
r
B(z,t)  B0 sin(kz  t)(φ
i)
r
B(z,t)  B0 sin(kz  t)kφ
r
φ
B(z,t)  B0 sin(kz  t)(k)
P36 - 15
Concept Q. Ans.: EM Wave
r
i
Answer: 1. B(z,t)  B0 sin(kz  t)φ
From the argument of the sin(kz   t) , we know
the wave propagates in the negative z-direction.
So we have Ê ´ B̂ = ĵ ´ ? = -k̂ Þ B̂ = î
P36 - 16
Concept Question: Capacitor
The figures above show a side and top view of a capacitor with
charge Q and electric and magnetic fields E and B at time t. At
this time the charge Q is:
1.
2.
3.
4.
Increasing in time
Constant in time.
Decreasing in time.
Not enough information given to determine how Q is changing.
P36 - 17
Concept Q. Answer: Capacitor
Answer: 3. The charge Q is decreasing in time
Use the Ampere-Maxwell Law. Choose positive unit normal out
of plane. Because the magnetic field points clockwise line
integral is negative hence positive electric flux (out of the plane
of the figure on the right) must be decreasing. Hence E is
decreasing. Thus Q must be decreasing, since E is proportional
to Q.
P36 - 18
Concept Question: Capacitor
The figures above show a side and top view of a capacitor with
charge Q and electric and magnetic fields E and B at time t. At
this time the energy stored in the electric field is:
1. Increasing in
2. Constant in time.
3. Decreasing in time.
P36 - 19
Concept Q. Answer: Capacitor
Answer: 1. The the energy stored in the electric field is
increasing in time
The direction of the Poynting Flux S (= E x B) inside the
capacitor is inward. Therefore electromagnetic energy is
flowing inward, and the energy in the electric field inside is
increasing.
P36 - 20
Concept Question: Inductor
The figures above show a side and top view of a solenoid
carrying current I with electric and magnetic fields E and B at
time t. The current I is
1. increasing in time.
2. constant in time.
3. decreasing in time.
P36 - 21
Concept Question Answer: Inductor
Answer: 3. The current I is decreasing in time
Use Faraday’s law. Choose positive unit normal out of plane.
Because the electric field points counterclockwise line integral
is positive, therefore the positive magnetic flux must be
decreasing (out of the plane of the figure on the right). Hence B
is decreasing. Thus I must be decreasing, since B is
proportional to I.
P36 - 22
Concept Question: Inductor
The figures above show a side and top view of a solenoid
carrying current I with electric and magnetic fields E and B at
time t. The energy stored in the magnetic field is
1. Increasing in time
2. Constant in time.
3. Decreasing in time.
P36 - 23
Concept Question Answer: Inductor
Answer: 3. The energy stored in the magnetic field is
decreasing in time.
The Poynting Flux S (= E x B) inside the solenoid is directed
outward from the center of the solenoid. Therefore EM energy is
flowing outward, and the energy stored in the magnetic field
inside is decreasing.
P36 - 24