electricity and magnetism ii griffiths chapter 9 em waves clicker questions 9.1

Electricity and Magnetism II Griffiths Chapter 9 EM Waves Clicker Questions 9.1

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

The complex exponential, is equal to: A) 0 B) i C) 1 D) E) Something else 9.3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

What does Faradays law tell us? Given the wave solutions 9.26

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

D2L 9.28

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

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

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

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

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

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

In linear dielectrics, A)Yes always. B) No, never. C) Sometimes yes, sometimes no. Depends on details of the dielectric. 9.36

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

For an electric plane wave given by The Poynting vector is given by (And, ) (Surprise?! Its not ~[Re(E)]^2 !) 9.62

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

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

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

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

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

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

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

If we are pigheaded, we can proceed with cos 2 imaginary, so Can we interpret this? 1 2 11 z x 9.71

The square root of a + bi is D. It is not defined E. Something else (this is harder than it looks) 9.72

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

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

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

For a good conductor, Is the B field A)Leading B) Lagging C) Matching D) It depends! the E field. 9.76

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

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

electricity and magnetism ii griffiths chapter 9 em waves clicker questions 9.1

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