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Sequences (1)

Students calculate electrostatic fields (\(V\), \(\vec{E}\)) and magnetostatic fields (\(\vec{A}\), \(\vec{B}\)) from charge and current sources with a common geometry. The sequence of activities is arranged so that the mathematical complexity of the formulas students encounter increases with each activity. Several auxiliary activities allow students to focus on the geometric/physical meaning of the distance formula, charge densities, and steady currents. A meta goal of the entire sequence is that students gain confidence in their ability to parse and manipulate complicated equations.

Ingredients (7)

Small Group Activity

5 min.

Events on Spacetime Diagrams
Students practice identifying whether events on spacetime diagrams are simultaneous, colocated, or neither for different observers. Then students decide which of two events occurs first in two different reference frames.
In this lecture, students see a geometric derivation of the Lorentz Transformation on a spacetime diagram.

Small Group Activity

30 min.

Mass is not Conserved

Groups are asked to analyze the following standard problem:

Two identical lumps of clay of (rest) mass m collide head on, with each moving at 3/5 the speed of light. What is the mass of the resulting lump of clay?

Small Group Activity

30 min.

Right Angles on Spacetime Diagrams
Students take the inner product of vectors that lie on the spacetime axis to show that they are orthogonal. To do the inner product, students much use the Minkowski metric.
A short improvisational role-playing skit based on the Star Trek series in which students explore the definition and notation for position vectors, the importance of choosing an origin, and the geometric nature of the distance formula. \[\vert\vec{r}-\vec{r}^\prime\vert=\sqrt{(x-x^\prime)^2+(y-y^\prime)^2-(z-z^\prime)^2}\]

Small White Board Question

10 min.

Time Dilation
Students answer conceptual questions about time dilation and proper time.
Students act out the classic light clock scenario for deriving time dilation.