7.1.3: Problems
- Page ID
- 33370
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Exercise \(\PageIndex{1}\): Electric field vs. magnetic field
The animation represents a traveling electromagnetic wave in the \(z\) direction. You can click-drag to the right or left to rotate about the \(z\) axis. Click-drag up or down to rotate in the \(xy\) plane. Restart. Which wave is the electric field and which one is the magnetic field?
Note that both the electric and magnetic fields in this animation are drawn with equal magnitude so you can see both fields. In reality, the magnetic field would be a factor of \(c\) smaller than the electric field in MKS units.
Problem authored by Melissa Dancy and Wolfgang Christian.
Exercise \(\PageIndex{2}\): Animation A is green light, what is Animation B?
Two animations represent traveling electromagnetic waves in the \(z\) direction. You can click-drag to the right or left to rotate the animations about the \(z\) axis. Click-drag up or down to rotate in the \(xy\) plane. If Animation 1 represents green light, what is represented by Animation 2? Restart.
Problem authored by Melissa Dancy and Wolfgang Christian.
Exercise \(\PageIndex{3}\): Which animation represents which color?
Three animations represent traveling electromagnetic waves in the \(z\) direction. You can click-drag to the right or left to rotate the animations about the \(z\) axis. Click-drag up or down to rotate in the \(xy\) plane. Restart. If green light, red light, and violet light are represented by the three animations, which of the animations represents which color?
Problem authored by Melissa Dancy and Wolfgang Christian.
Exercise \(\PageIndex{4}\): Characterize the electromagnetic wave
By moving the slider, you can change the position of the square in the electromagnetic wave animation. Then you can view the graph on the right, which shows you the field-vector representation of the electric field (position is given in microns [\(10^{-6}\) meters] and time is given in femtoseconds [\(10^{-15}\) seconds]). The animation only shows you the electric field. Restart.
- In what direction is the magnetic field?
- What are the wavelength, frequency, and speed of the electromagnetic wave represented here?
Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian, Melissa Dancy, and Anne J. Cox.
Exercise \(\PageIndex{5}\): Characterize the electromagnetic wave
By moving the slider, you can change the position of the square in the electromagnetic wave animation. Then you can view the graph on the right which shows you the field-vector representation of the electric field (position is given in millimeters and time in picoseconds [\(10^{-12}\) seconds]). The animation only shows you the electric field. Restart.
- In what direction is the magnetic field?
- What are the wavelength, frequency, and speed of the electromagnetic wave represented here?
Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian, Melissa Dancy, and Anne J. Cox.
Exercise \(\PageIndex{6}\): Field produced by oscillating charge
The animation shows how static electric field lines from a positive point charge produce a radiation field if the charge is caused to oscillate. Initially the charge is stationary. Restart.
Start the Charge Oscillating: Notice how the electric field lines form waves that move away from the charge when the charge is oscillating.
- What is the direction of the magnetic field associated with the waves to the right of the charge?
- In what direction is the radiation field a maximum?
Problem authored by Melissa Dancy.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.