## Exploration 32.2: Plane Waves and the Electric Field Equation

You can change the position of the square (that shows you the field-vector representation of the electric field), as well as the maximum value of the electric field and the wavelength (position is given in meters and time is given in nanoseconds). Restart.

The electromagnetic plane wave in the animation above is described by the equation

E (z, t) = Emax sin (k z - ω t) i,

where k = 2π/λ (λ is the wavelength) and ω = 2πf (f is the frequency).

1. Explain why the equation is a function of z and t for this wave.
2. Why is this equation a vector equation with a component in the x direction?
3. What is the associated equation for the magnetic field (check in your book if needed)?
4. What do you predict will happen in both representations (the vector field view to the right and the wave view to the left) if you increase the amplitude? Change the amplitude to check your prediction. Did the frequency change? Why or why not?
5. What do you predict will happen in both representations if you increase the wavelength? Try it. This time did the frequency change? Why or why not?
6. Pick a value of the wavelength (λ) and measure it.
7. Measure the frequency (f) at this wavelength.
8. What is the value of λf? (It should be 3 x 108 m/s).

Note: When you change the wavelength, you need to let the animation play long enough for the old wavelength to disappear from the axis by letting the animation run for 100--200 ns before making any measurements.

Exploration authored by Anne J. Cox.
Script authored by Wolfgang Christian, Melissa Dancy, and Anne J. Cox.