Electricity and Magnetism II Griffiths Chapter 9 EM Waves Clicker Questions 9.1
Transcript
Slide 1
Electricity and Magnetism II Griffiths Chapter 9 EM Waves
Clicker Questions 9.1
Slide 2
A function, f(x,t), satisfies this PDE: Invent two different
functions f(x,t) that solve this equation. Try to make one of them
boring and the other interesting in some way. 9.2
Slide 3
The complex exponential, is equal to: A) 0 B) i C) 1 D) E)
Something else 9.3
Slide 4
A function, f, satisfies the wave equation: A) Sin( k(x vt)) B)
Exp( k(-x vt )) C) a( x + vt ) 3 D) All of these. E) None of these.
Which of the following functions work? 9.4
Slide 5
A function, f, satisfies the wave equation: A) Sin( k(x vt)) B)
Exp( k(-x vt )) C)a( x + vt ) 3 D) All of these. E) None of these.
Which of the following functions work? In fact, ANY function f ( x
+/- vt ) is a good solution!! Shape travels left (+) or right (-).
9.5
Slide 6
A right moving solution to the wave equation is: f R (z,t) = A
cos(kz t + ) Which of these do you prefer for a left moving soln?
A) f L (z,t) = A cos(kz + t + ) B) f L (z,t) = A cos(kz + t - ) C)
f L (z,t) = A cos(-kz t + ) D) f L (z,t) = A cos(-kz t - ) E) more
than one of these! (Assume k, , are positive quantities) To think
about; Is(are) the answer(s) really just preference (i.e. human
convention) or are we forced into a choice? 9.6
Slide 7
Two different functions f 1 (x,t) and f 2 (x,t) are solutions
of the wave equation. A) Yes, always B) No, never. C) Yes,
sometimes, depending of f 1 and f 2. Is (A f 1 + B f 2 ) also a
solution of the wave equation? 9.7
Slide 8
Two traveling waves 1 and 2 are described by the equations: y 1
(x,t) = 2 sin(2x t) y 2 (x,t) = 4 sin(x 0.8 t) All the numbers are
in the appropriate SI (mks) units. Which wave has the higher speed?
A) 1B) 2C) Both have the same speed. 9.8
Slide 9
A) B) C) D) Two impulse waves are approaching each other, as
shown. Which picture correctly shows the total wave when the two
waves are passing through each other? 9.9
Slide 10
A solution to the wave equation is: f(z,t) = A cos(kz t + )
What is the speed of this wave? Which way is it moving? If is small
(and >0), is this wave delayed or advanced? What is the
frequency? The angular frequency? The wavelength? The wave number?
9.10
Slide 11
A solution to the wave equation is: f(z,t) = Re[A e (kz t + ) ]
What is the speed of this wave? Which way is it moving? If is small
(and >0), is this wave delayed or advanced? What is the
frequency? The angular frequency? The wavelength? The wave number?
9.11
Slide 12
A complex solution to the wave equation in 3D is: What is the
speed of this wave? Which way is it moving? Why is there no ? What
is the frequency? The angular frequency? The wavelength? The wave
number? 9.12
Slide 13
Is "The Wave" at the stadium a transverse wave or a
longitudinal wave? A) TransverseB) Longitudinal C) neither A wave
on a stretched drum head is an example of a A) Transverse waveB)
Longitudinal wave C) it's not a wave at all 9.13
Slide 14
A solution to the wave equation is: f(z,t) = Re[A e i(kz t + )
] If is small (and >0), is this wave delayed or advanced
compared to e i(kz t ) ? A) delayed B) advanced C) neither, depends
on values of z and t. delayed advanced 9.14
Slide 15
The electric field for a plane wave is given by: A)The
direction of the electric field vector. B) The direction of the
magnetic field vector. C) The direction in which the wave is not
varying. D) The direction the plane wave moves. E) None of these.
The vector k tells you: 9.15
Slide 16
The electric field for a plane wave is given by: A)The
direction of the electric field vector. B) The speed of the
traveling wave. C) The direction the plane wave moves. D) A
direction perpendicular to the direction the plane wave moves E)
None of these/MORE than one of these/??? The vector k tells you:
9.16
Slide 17
The electric field for a plane wave is given by: A)The x
direction. B) The radial (r) direction C) A direction perpendicular
to both k and x D) The k direction E) None of these/MORE than one
of these/??? Suppose E 0 points in the +x direction. Which
direction is this wave moving? 9.17
Slide 18
One particular traveling wave solution to this is f 1 (z,t) = A
1 cos(k 1 z 1 t + 1 ) This wave has speed v = 1 /k 1 (do you see
why?) There are many other solutions, including f 2 (z,t) with the
SAME functional form, but with higher frequency, 2 > 1. What can
you say about the speed of that new solution? A) greater than v B)
less than v C) equal to v D) indeterminate! The 1-D wave equation
is By the way: This wave travels rightward (do you see why?) This
wave has wavelength lambda= 2/k 1 (do you see why?) This wave has
period 2 / 1 (do you see why?) 9.18
Slide 19
One particular traveling wave solution to this is often written
This wave travels in the k direction (do you see why?) This wave
has wavelength lambda= 2/|k| (do you see why?) This wave has period
2/ (do you see why?) This wave has speed v = /|k| (do you see why?)
What is the real form of this wave? The 3-D wave equation is
9.19
Slide 20
A wave is moving in the +z direction: f(x, y, z, t) = Re[A e
i(kz t + ) ] The value of f at the point (0,0,z 0, t) and the point
at (x, y, z 0, t) are related how? f 1 = f (0,0,z 0, t) vs. f 2 =
f(x, y, z 0, t) A)f 1 = f 2 always B) f 1 > or < or = f 2
depending on the value of x,y z x y f1f1 f2f2 9.20
Slide 21
Here is a snapshot in time of a longitudinal wave: The
divergence of this field is: A)Zero B)Non-zero C)Impossible to tell
without further information 9.21
Slide 22 k 2. Which wa"> k 2. Which wave has the larger
frequency f? A) Wave 1 B) Wave 2 C) impossible to tell 9.22"> k
2. Which wa" title="The electric fields of two E/M waves in vacuum
are both described by: The "wave number" k of wave 1 is larger than
that of wave 2, k 1 > k 2. Which wa">
The electric fields of two E/M waves in vacuum are both
described by: The "wave number" k of wave 1 is larger than that of
wave 2, k 1 > k 2. Which wave has the larger frequency f? A)
Wave 1 B) Wave 2 C) impossible to tell 9.22
Slide 23
The electric field of an E/M wave is described by k = 0.1 m -1,
at x=1m and t=0, what is the direction of the B-field? A) +x B) +y
C) x D) +z E) -z 9.23
Slide 24
You have this solution to Maxwells equations in vacuum: If this
wave travels in the y direction, is polarized in the x direction,
and has a complex phase of 0, what is the x component of the
physical wave? To think about: What is the y component? What would
change if the complex phase of E 0 was 90 0 ? -90 0 ? 9.24
Slide 25
E) None of these. What does this mean, in words? Think about
the first of Maxwells Equations (Gausss Law) in vacuum: Try a
complex exponential linearly polarized plane wave: Then, Gausss Law
becomes: 9.25
Slide 26
What does Faradays law tell us? Given the wave solutions
9.26
Slide 27
An electromagnetic plane wave propagates to the right. Four
vertical antennas are labeled 1-4. 1,2, and 3 lie in the x-y plane.
1,2, and 4 have the same x-coordinate, but antenna 4 is located
further out in the z-direction. Rank the time-averaged signals
received by each antenna. A)1=2=3>4 B) 3>2>1=4 C)
1=2=4>3 D) 1=2=3=4 E) 3>1=2=4 1 y z x 4 3 2 9.27
Slide 28
D2L 9.28
Slide 29
9.29
Slide 30
A plan wave approaches the eye and some of the light rays in
the wave enter the eye's pupil. No other rays enter the eye. What
does the eye see? A) A single point of light, surrounded by
blackness. B) A uniformly illuminated wall of light, like a white
wall. C) Many scattered points of light, like stars in the night
sky. D) None of these Eye 9.30
Slide 31
A) B) C) D) E) None of these detector a d PoPo R A point source
of radiation emits power P o isotropically (uniformly in all
directions). A detector of area a d is located a distance R away
from the source. What is the power p received by the detector?
9.31
Slide 32
For a plane electromagnetic wave in vacuum: E k B k E B E, B in
phase B = E/c k E B Which of Maxwells equations requires that B k ?
Which of Maxwells equations requires that B = E/c ? 9.32
Slide 33
Two radio dishes (shaped like bowls) are receiving signals from
a radio station which is sending out radio waves in all directions
with power P. Dish 2 is twice as far away as Dish 1, but has twice
the diameter. Which dish receives more power? (Dish 2 is not in the
shadow of Dish 1.) A: Dish 1B: Dish 2 C: Both receive the same
power Dish 1 Dish 2 9.33
Slide 34
D c R A parabolic dish focuses the EM radiation from a source
into a beam of constant diameter D : The intensity of the light in
the beam falls with distance R as: A)I ~ 1/R 2 B)I ~ 1/R C) I =
constant D) Something else 9.34
Slide 35
When a jet flies faster than the speed of sound, there is...
A)a sonic boom occurring only at the moment that the jet exceeds
the speed of sound. B) a continuous sonic booming occurring all the
time that the jet is going faster than Mach 1. 9.35
Slide 36
In linear dielectrics, A)Yes always. B) No, never. C) Sometimes
yes, sometimes no. Depends on details of the dielectric. 9.36
Slide 37
In a non-magnetic, linear dielectric, How does v compare to c?
A)v > c always B)v < c always C)v > or < c depending on
9.37
Slide 38
A plane wave normally incident on an interface between 2 linear
(non-magnetic) dielectrics (n 1 n 2 ) 12 EIEI v1v1 BIBI ETET v2v2
BTBT ERER v1v1 BRBR z x How do k 1 and k 2 compare? How do 1 and 2
compare? A)k1=k2, 1= 2B) k1 k2, 1 2 C) k1 = k2, 1 2D) k1 k2, 1 = 2
9.38
Slide 39
For an electric plane wave given by A. The E and B fields are
at maximum value at the same time B. The B field maximum lags the E
field by a quarter period C. The B field maximum leads the E field
by a quarter period D. The E and B field maxima are exactly a half
period apart E. Not enough information to tell the magnetic field
is required by Faradays law to be where Which of the following is
true at a particular point in space? 9.39
Slide 40
Wave on a 1D string, hitting a boundary between 2 strings of
different speeds: Boundary conditions (continuity) give the
results: Is the transmitted wave in phase with the incident wave?
A) Yes, always B) No, never C) Depends Why? How do you decide?
9.40
Slide 41
Wave on a 1D string, hitting a boundary between 2 strings of
different speeds: Boundary conditions (continuity) give the
results: Is the reflected wave in phase with the incident wave? A)
Yes, always B) No, never C) Depends Why? How do you decide?
9.41
Slide 42
Below is an idealized picture of a traveling EM plane wave. It
is a snapshot at t=0. (Wavelength is given, as is E 0.) Write down
a pair of mathematical formulae which describe this wave (in
complex form) for all times. (One for E and B) y z x X= E0E0
9.42
Slide 43
With spatially varying (r), plane EM waves of the form, are: A)
No longer good solutions to Maxwells Eqs. B) No longer have the
same C) Are unchanged from the vacuum case. D) Are no longer
transverse. E) None of the above. 9.43
Slide 44
In matter, we have If there are no free charges or currents,
can we argue A)Yes, always B)Yes, under certain conditions (what
are they?) C)No, in general this will NOT be true! D)?? 9.44
Slide 45
In matter with no free charges or currents, we have: A) Fig 1
goes with i and iii (i.e. the ones involving D and E), Fig 2 goes
with ii and iv ( B and H) B) Fig 1 goes with i and ii ( div), Fig 2
goes with iii and iv ( curl) C) Fig 1 goes with ii only ( B field),
Fig 2 goes with iii only ( E field) D) Something else! E) Frankly,
I dont really understand this question. Fig 1 Fig 2 To figure out
formulas for boundary conditions, match the picture to the PDE(s)
above. 9.45
Slide 46
Match the Maxwell equation (i-iv) in matter (no free charges)
with the corresponding boundary condition (1-4) it generates: A)i
4, ii 3 iii 2 iv 1 B) i 2, ii 1 iii 4 iv 3 C) Wait, only SOME of
the BCs on the right are correct! D) Wait, NONE of the BCs on the
right are correct! E) Frankly, I dont really understand this
question. Region 1 Region 2 9.46
Slide 47
Match the Maxwell equation (i-iv) in matter (no free charges)
with the corresponding boundary condition (1-4) it generates: B) i
2, ii 1 iii 4 iv 3 Region 1 Region 2 9.47
Slide 48
An EM plane wave in free space comes from the left towards an
interface. Which statement is true? A) Only certain frequencies are
allowed. B) You are free to choose the wave speed. C) A
compensating wave must travel towards the interface from the right
too. D) You may independently select the frequency and the
k-vector. E) None of the above. 9.48
Slide 49
An EM plane wave in free space comes from the left towards an
interface. Which statement is true? A) Only certain wave speeds are
allowed. B) You are free to choose k. C) A reflected wave on the
left and a transmitted wave on the right may travel away from the
interface too. D) All of the above. E) None of the above. 9.49
Slide 50
For linear materials, we found that the index of refraction n
is given by: Can n be less than one? A. Yes B. No 9.50
Slide 51
For our reflected and transmitted waves, how many unknowns have
we introduced? A.2 B.4 C.8 D. 12 E. None of the above 9.51
Slide 52
For our reflected and transmitted waves, how many unknowns have
we introduced? A.2 B.4 C.8 D. 12 E. None of the above 9.52
Slide 53
An EM plane wave comes from the left towards an interface.
Reflected and transmitted waves leave. Therefore, the total E-field
is like: A) True. B) False. C) Dont understand and have questions
D) Too confused for questions... 9.53
Slide 54
An EM plane wave comes from the left towards an interface.
Reflected and transmitted waves leave. Therefore, at the interface
we expect to match the waves with something like: A) No. This type
of condition cannot work. B) No. This is mathematically possible,
but physically incorrect. C) Ah, therefore I see a necessary
condition D) None of these. 9.54
Slide 55
A EM plane wave comes from the left. Reflected and transmitted
waves leave. Therefore, at the interface we expect to match the
waves with something like: A) B) C) D) None of these. at the
interface, 9.55
Slide 56
Do plane waves in matter (see above) represent general
solutions of Maxwells Equations? A) Yes! Fixed k-vector and
frequency are predicted via Fourier superposition. B) No. In some
cases you would need complex k-vectors, which is unphysical. C) No.
In some cases you would need frequency dependent or . Then plane
waves dont work. D) No. In spatially varying material, you might
need non-transverse plane waves and thats unphysical. E) None of
the above. 9.56
Slide 57
In matter without any free charge density, I can conclude that
A. Divergence of D and E are zero B. Divergence of D is zero and
divergence of E may be zero C. Divergence of D and E are not zero
D. Divergence of D may be zero and divergence E is zero E. Not
enough information to tell 9.57
Slide 58
In the case where medium 1 had a very slow wave velocity and
medium 2 had a much higher wave velocity, 2 v 2 >> 1 v 1.
Assuming that the permeabilities (s) are essentially equal to the
permeability of the vacuum, what is the relation between 1 and 2 ?
A. 1 2 B. 1 > 2 C. 1 < 2 D. Not enough information to tell
9.58
Slide 59
For our reflected and transmitted waves, we found that R = T =
I. What can we now conclude about the wavelengths of the
transmitted and reflected waves? A. R = T = I B. R = T I C. R T = I
D. R = I T E. Need more information 9.59
Slide 60
What gives a large transmission of light at normal incidence?
A)When v 1 >>v 2 B)When v 2 >>v 1 C)When v is very
different in the two media D)When v is nearly the same in the two
media E)None of these/other/Im confused/ For light at normal
incidence, we found: 9.60
Slide 61
For an electric plane wave given by A. B. C. D. E. More than
one of the above is true The contribution from the E field to the
(real) energy density u EM is 9.61
Slide 62
For an electric plane wave given by The Poynting vector is
given by (And, ) (Surprise?! Its not ~[Re(E)]^2 !) 9.62
Slide 63
An ideal (large) capacitor has surface charge density + on its
top plate and on its bottom plate. There is only vacuum between the
plates. What is E inside the capacitor ? A)E = / B) E = -/ C) E =
/2 D) E = -/2 None of the above + - 9.63
Slide 64
An ideal (large) capacitor has surface charge density + on its
top plate and on its bottom plate. Now a linear dielectric with
permittivity is inserted between the plates. How does E inside the
dielectric compare with the case with no dielectric? A) E is
smaller B) E is the same C) E is larger D) Depends on the of the
dielectric Not enough information to tell + - 9.64
Slide 65
In the case where medium 1 had a very slow wave velocity and
medium 2 had a much higher wave velocity, we found that R 1 and T
0. In the opposite case, where the wave velocity in medium 1 is
much higher than that in 2, we expect A.R 1, T 0 B.R 0, T 1 C.R
1/2, T 1/2 D. Not enough information to tell 9.65
Slide 66
A.0 B.90 C.180 D.Can be more than one of the above E.Depends on
the incident angle and dielectric properties What is the relative
phase angle between the incident wave and the transmitted wave?
9.66
Slide 67
To reduce glare off the lake, should the polarization axis of
these sunglasses be A)Vertical B) Horizontal C) Makes no difference
D) ???? 9.67
Slide 68
Slide 69
What is the power/m 2 striking the boundary wall? A)Still B)
cos 1 C) /cos 1 D) Something else! (sin 1 or cos 2 1 or cos 2, or )
1 2 11 The power/m 2 passing Here is 9.69
Slide 70
Our general solution for the transmitted wave is Snells law
tells us If n 2 < n 1, there is a critical angle,, beyond which
there is no real solution for 2. How should we interpret this lack
of solution physically? 1 2 11 9.70
Slide 71
If we are pigheaded, we can proceed with cos 2 imaginary, so
Can we interpret this? 1 2 11 z x 9.71
Slide 72
The square root of a + bi is D. It is not defined E. Something
else (this is harder than it looks) 9.72
Slide 73
We have a traveling wave solution satisfies where the (complex)
wave vector True (A) or False (B): This traveling wave is
transverse. (Or C) I have no good idea what that means) 9.73
Slide 74
The magnetic field amplitude in a metal associated with a
linearly polarized electric EM wave is True (A) or False (B):The B
field is in phase with the E field. (C) It depends! 9.74
Slide 75
The magnetic field amplitude in a highly conductive metal
(>>) associated with a linearly polarized electric EM wave is
True (A) or False (B): The B field is in phase with the E field.
(C) It depends! 9.75
Slide 76
For a good conductor, Is the B field A)Leading B) Lagging C)
Matching D) It depends! the E field. 9.76
Slide 77
If E x (x,y,z,t)=E 0 exp[i (kz-t)], and you have a free charge
q which responds to this E field, (F=qE) what can you say about the
relative phase of v(t) and E(t) at any point in space? A)They are
in phase B)They are 90 out of phase C)They are 180 out of phase D)I
dont really know what this means E)Something else 9.77
Slide 78
The Fresnel equation (for normal incidence) is If region 2 is a
conductor, n 2 = (c/) k 2 is complex! But, recall that for a good
conductor, /k R