Homework

- Reading Preparation
- Key Equations
- WebLecture
- Study Activity
- Chat Preparation Activities
- Chapter Quiz
- Lab Work

**Text Reading**: Giancoli, *Physics - Principles with Applications*, Chapter 22: 1-7 (All)

*Section 1*Maxwell's equations sum up the relationship between charge and magnetism.*Section 2*Because changing electrical fields produce changing magnetic fields, and changing magnetic fields produce changing electrical fields, a wire with changing current will produce electromagnetic waves that propagate indefinitely. The electromagnetic wave derives from the E and B changing fields, acting at right angles to each other.*Section 3*Theoretically, electromagnetic waves range from 0 to infinity in length, or from 0 to infinite frequency. In practice, we can detect EM waves in the range from less than 60 Hz (60 cycles/second, wavelength around 5 million meters) to greater than 10^{20}Hz (less than 3 * 10^{-12}m). Visible light lies in the range 4-7.5*10^{14}Hz, or 7.5-4*10^{-7}m. The velocity of EM waves depends on the permittivity of the electrical field in a medium and the permeability of the magnetic field to that medium.*Section 4*Maxwell realized that the speed of EM predicted by the permittivity/permeability values matched Roemer's speed of light. Michelson's measurements for the speed of light were more accurate than Roemer's; the value is now given as 2.99792458 * 10^{8}m or 3 * 10^{8}m/s for ease of use.*Section 5*A light wave carries energy, so the space through which light is propagated has a potential energy state u = 1/2 ε_{0}E^{2}+ 1/2 B^{2}/μ_{0}. Because B = E/c, we can write the B field contribution in terms of E (u = ε_{0}E^{2}) or the E field contribution in terms of B (u = B^{2}/μ_{0}), or as a single term: u = √[BE*(ε_{0}/μ_{0})].

We can also evaluate the intensity of the energy: I = power/area = (energy/time) / area = (ΔU/Δt) /A*Section 6*Since EM waves carry energy (U = E = 1/2mv^{2}), they carry linear momentum (p = mv), and therefore have a related force (F = Δp/Δt) which can be analyzed in terms of pressure (P = F/A). This radiation pressure is the amount of energy transferred when a beam of light is completely absorbed by an object: Δp = ΔU/c.*Section 7*A key fundamental law is that waves add up. We can put one EM signal (information content from a program) on top of another signal (a signal of constant frequency called the*carrier signal*). Instruments can detect and isolate wave combinations identified carrier signals, which makes radio and TV possible.

- Displacement current: $$\sum {B}_{\text{\u2551}}\text{}\Delta l\text{}=\text{}{\mu}_{0}(I\text{}+\text{}{I}_{D})$$ $${I}_{D}\text{}=\text{}\frac{\Delta Q}{\Delta t}\text{}={\u03f5}_{0}\frac{\Delta {\Phi}_{E}}{\Delta t}\text{}$$
- Ampère's law using Electric Flux: $$\sum {B}_{\text{\u2551}}\text{}\Delta l\text{}=\text{}{\mu}_{0}I\text{}+\text{}{{\mu}_{0}\u03f5}_{0}\frac{\Delta {\Phi}_{E}}{\Delta t}$$
- Speed of light, permeability and permissivity: $$c\text{}=\text{}\frac{1}{\sqrt{{{\mu}_{0}\u03f5}_{0}}}\text{}=\text{}2.99792458\text{}\ast \text{}{10}^{8}\text{}\frac{m}{s}$$
- Energy carried by EM Wave: $$u\text{}=\text{}{\u03f5}_{0}{E}^{2}\text{}=\text{}\frac{{B}^{2}}{{\mu}_{0}}\text{}=\text{}\sqrt{\frac{{\u03f5}_{0}}{{\mu}_{0}}}\text{}\mathrm{EB}$$
- Radiation Pressure $$P\text{}=\text{}\frac{F}{A}\text{}=\frac{1}{A}\text{}\frac{\Delta p}{\Delta t}\text{}=\frac{1}{A}\text{}\frac{\Delta U}{c\Delta t}\text{}=\frac{{I}_{\mathrm{avg}}}{c}\text{}[\mathrm{Full}\text{}\mathrm{absorption}]\text{}\mathrm{or}\text{}2\frac{{I}_{\mathrm{avg}}}{c}\text{}[\mathrm{Full}\text{}\mathrm{reflection}]\text{}$$

**Read the following weblecture before chat**: Maxwell's Elegant Laws

Use the simulation for Gauss's Law to visualize electric flux through a sphereical boundary.

**Forum question**: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer**before**chat starts for this session.**Mastery Exercise**: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

**Required**: Complete the Mastery exercise with a passing score of 85% or better.- Go to the Moodle and take the quiz for this chat session to see how much you already know about astronomy!

If you want lab credit for this course, you must complete at least 12 labs (honors course) or 18 labs (AP students). One or more lab exercises are posted for each chapter as part of the homework assignment. We will be reviewing lab work at regular intervals, so do not get behind!

**Lab Instructions**: Measuring the Speed of Light

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