Name:
Honor Code:
Instructions
You may use the course book, your video notes, challenge problems, other notes.
Pasting screenshots into an AI tool is … not allowed.
1. Fitness of units
1.1. Warmup power play
What are the units of power density p?
Show this by working out the units of the right side of \(\eqref{epower}\) from their SI base units.
1.2. You spin me round
The gyroradius or Larmor radius of the circular path of a charged particle traveling in a magnetic field is
You would reasonably assume that radius \(\rho\) is in length units, specifically meters. Analyze the units of the quantities on the right side of \(\eqref{gyro}\) to show that the right side does indeed reduce to units of meters only.
1.3. History is memory
The magnetic hysteresis curve shown in the figure is also called a B-H curve. A curious aspect of this relationship is the fact that, for some materials, the curve traces out an area instead of just some curved path.
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What are the SI base units of the area of a closed loop on a B-H plot? (B-C-D-E-F-G-B)
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Also, show how these units can also be expressed in the more useful form of energy per volume, J / m3.
2. Wires move?
Consider a length of power cord or speaker cable having two conductors and carrying 10 ARMS of AC current. Thanks to KCL and current flowing in closed loops, the current flowing in one conductor is the same amount flowing in the adjacent conductor but opposite direction.
What can you measure about this situation without using an ammeter (breaking the circuit to insert the instrument in series)?
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Can you measure the current using a force gauge? Describe clearly how to set up an experiment to make this measurement using "first principles", i.e. using the laws taught so far in the course.
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How else can you infer the current flow in the cable?
3. Fake current
Describe the difference between current density (J) and displacement current and what makes the latter so important.
4. You nits
| Symbol | Name | Unit(s) name, symbol |
|---|---|---|
\(Q\) |
charge |
coulombs, C |
\(\vec{F}\) |
force vector |
newtons, N, kg / (m · s2) |
\(\vec{E}\) |
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\(\rho_V\), \(\rho_S\), \(\rho_L\) |
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\(\epsilon_0\) |
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\(\epsilon_r\) |
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\(\epsilon\) |
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\(W_e\) |
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\(V\) |
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\(\vec{P}\) |
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\(\rho_p\) |
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\(\vec{D}\) |
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\(\chi_e\) |
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\(C\) |
capacitance |
farads, F |
\(E_{DS}\) |
dielectric strength |
volts per meter, V/m |
\(I\) |
current |
A, amperes, amps, coulombs per sec, C/s |
\(\vec{J}\) |
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\(\sigma\) |
conductivity |
siemens/meter, S/m, (Ω·m)-1 |
\(\rho\) |
resistivity |
Ohm-meters, Ω·m |
\(p\) |
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\(\vec{B}\) |
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\(\mu_0\) |
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\(\vec{m}\) |
magnetic dipole moment |
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\(\vec{F}\) |
force |
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\(\tau\) |
torque |
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\(\vec{A}\) |
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\(\vec{A}\) |
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\(\chi_m\) |
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\(\mu_r\) |
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\(\vec{H}\) |
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\(\Psi_m\) |
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\(\mathcal{R}\) |
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\(N\cdot I\) |
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\(\Lambda\) |
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\(M_{jk}\) |
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\(L\) |
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\(\vec{S}\) |
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\(c\) |
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\(\vec{J}_c\) |
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\(\vec{J}_d\) |
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5. The vocation’s vocabulary
Begin from the list of quantities, symbols, and units encountered in the course thus far.
Add to this list all of the named laws and properties you’ve studied. Include the name, formula, at minimum. (The number of lines in the table is not significant.)
Start with all of the relationships that have the form: A = constant · C, then the various Laws.
| Name | Formula + other |
|---|---|
6. Cohere into a connected whole
Summarize the course’s content so far: Draw a concept map of the terminology, concepts, and connections.
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Examples electronics-world, voltage-current, semiconductor-physics.
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Use the free tool Cmap Cloud, or draw your own in a similar style. [1]
Because this is the second iteration of a concept map, your new map should:
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Begin with the map you created for Review 1.
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Improve and update the existing content to reflect a better organization and understanding of those concepts.
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Extend the map with the concepts covered after Review 1.
7. Problem maker
Consider the list of § 7.1.
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Use the random number generator tool to select a random learning objective.
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Create a problem whose solution demonstrates meeting the objective. (Pay attention to the objective’s verb.)
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Alternatively, show a situation where the objective’s concept shows up in a circuit / system / structure in real life.
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Solve the problem. At minimum describe the method for finding a solution and set up the solving thereof. (e.g. some geometries are difficult to compute the integrals for, but are real situations in current technologies)
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Do this for 12 unique objectives, beginning a fresh page each time.
7.1. Segment 2 Learning Objectives
Chapters 10 — 18
- Current flow and power density
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Calculate the total current flowing through a surface given the current density.
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Calculate the resistance, current, electric field, and current density in a material knowing the material composition, geometry, and applied voltage.
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Calculate the power density and total power when given the current density and electric field.
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- Magnetic fields and fluxes from currents
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Use Ampere’s Law to calculate magnetic fields near symmetrical electric currents.
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Design a solenoid or toroidal solenoid to achieve a required magnetic flux density.
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Calculate the magnetic flux density near one or more current-carrying line segments or loops.
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- Magnetic forces
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Calculate the force on a charged particle moving at a uniform speed through a magnetic field.
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Calculate the gyroradius of a charged particle injected into a region of magnetic flux density.
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Calculate the force between two current-carrying conductors.
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Calculate the torque on a loop of current in a constant magnetic field.
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- Magnetic materials
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Given the magnetic field intensity, polarization, or magnetic flux density, calculate the other two for a particular material.
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Analyze a magnetic circuit to determine the magnetic flux or magnetic flux density at a particular point in the circuit.
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- Induction and inductance
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Calculate the self-inductance of a conductor.
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Calculate the mutual inductance of multiple conductors.
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Calculate the energy stored in an inductor.
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Use Faraday’s Law of Induction to determine the magnitude and direction of the current induced in a coil that is subject to a time-varying magnetic flux.
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Calculate the voltage induced across a rotating loop of wire.
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Analyze a transformer to determine the voltage and current seen at the secondary coil given the turns ratio and the voltage/current on the primary coil.
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- Displacement current
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Use the continuity equation to determine how long it will take a fraction of charge inside a conductor to move to the surface.
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Given the conduction current in a lossy dielectric, calculate the displacement current density.
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Given the geometry and voltage of a capacitor, calculate the displacement current.
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Determine whether a material is a conductor or an insulator at a given frequency and calculate the frequency where the transition occurs.
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- Maxwell’s Equations and Poynting’s theorem
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Calculate the skin depth of a magnetic wave as it penetrates a solid material and the distance at which the wave will have decayed to a particular level.
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Given the electric and magnetic fields, calculate the magnitude and direction of the Poynting vector.
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Calculate the speed of light for a given material.
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