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class code: SPS21 teacher: Mr. Elert
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Physics A: Problem Set 20: Electromagnetism

recommended reading

High Marks: 3:122–3:126
Barron's Let's Review: 10.4–10.5
physics.info: Electromagnetism, Induction
Wikipedia: Electromagnetism, Lorentz force, Electromagnetic induction
Reference table with select items highlighted, page 1 Reference table with select items highlighted, page 2 Reference table with select items highlighted, page 3 Reference table with select items highlighted, page 4 Reference table with select items highlighted, page 5 Reference table with select items highlighted, page 6

classwork

  1. Which force fields surround…
    1. a stationary electron?
    2. a moving electron?
    1. A stationary electron is surrounded by…
      • a gravitational field, since all electrons have mass (9.11 × 10−31 kg)
      • an electric field, since all electrons have charge (−1.60 × 10−19 C)
      • a magnetic field, since all electrons have charge and are always spinning, even when they're sitting still
    2. A moving electron is surrounded by…
      • a gravitational field, since all electrons have mass
      • an electric field, since all electrons have charge
      • a magnetic field, since all electrons have charge and the problem explicitly says this one is going somewhere

homework

  1. Copy the mathematical expression below and paste it into the search field of Google or WolframAlpha. Hit enter and see what you get back.

    1/sqrt(electric constant*magnetic constant)

    1. Write the result of the calculation below. Include every digit. Don't forget to include a unit.
    2. Rewrite your answer to part a, but this time write it in scientific notation with only 3 significant digits. (It still needs a unit.)
    3. What scientifically important conclusion can you make from the result of this calculation? Keep your response short — let's say, no more than 12 words.

    Solutions

    1. 299,792,458 m/s
      This is the exact speed of light in a vacuum.
    2. 3.00 × 108 m/s
      This is the speed of light in a vacuum as it appears in your reference tables. It is good enough for the kind of work high school students do. It is also easier to say.
    3. Light is an electromagnetic wave.
      The electric constant (which describes the electric nature of empty space), the magnetic constant (which describes the magnetic nature of empty space), and the speed of light (which describes an essential property of light) are all related mathematically. Proof of this is beyond the scope of what high school students typically need to know.

    I asked ChatGPT to write an answer to the last question. I am not entirely satisfied with any of its responses. The last one is the best, but the answer would be better with 3 fewer words..

    • "The result is the speed of light in a vacuum."
    • "The speed of light is a universal constant in vacuum."
    • "The speed of light is a fundamental constant in physics."
    • "The calculation reveals the electromagnetic wave's fundamental property: speed of light."
    • "The calculation unveils the profound link between electricity and magnetism: the speed of light."
    • "Light is an electromagnetic wave with constant speed."

    ChatGPT (v 3.5), 2024

    For fun I asked ChatGPT to write an answer in the form of a Haiku.

    Electric and mag,
    Merge in waves through space and time,
    Light's speed, a constant.

    ChatGPT (v 3.5), 2024