Electromagnetic Waves — Practice Quiz

A Physics cheat sheet for Electromagnetic Waves — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Speed of Light: Relationship between speed \(c\), frequency \(f\), and wavelength \(\lambda\). \(c \approx 3.00 \times 10^8 m/s\).

$$c = f \lambda$$

Speed of Light (Maxwell): Speed of light related to permittivity \(\epsilon_0\) and permeability \(\mu_0\) of free space.

$$c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$$

Electric and Magnetic Fields: Relationship between magnitudes of electric field \(E\) and magnetic field \(B\) in an EM wave.

$$E = cB$$

Total Energy Density: Sum of electric and magnetic energy densities. \(u_{avg} = \epsilon_0 E_{rms}^2\).

$$u = \frac{1}{2} \epsilon_0 E^2 + \frac{1}{2 \mu_0} B^2$$

Intensity: Average power per unit area carried by the wave. \(S = c \epsilon_0 E_{rms}^2\).

$$S = c u_{avg}$$

Doppler Effect (EM Waves): Observed frequency \(f_o\) for source frequency \(f_s\) with relative speed \(v_{rel}\). (+ for approaching, - for receding).

$$f_o = f_s (1 \pm \frac{v_{rel}}{c})$$

Malus' Law: Intensity \(S\) of polarized light after passing through an analyzer at angle \(\theta\) to polarization direction.

$$S = S_0 \cos^2 \theta$$

Practice quiz

  1. A radio station broadcasts at a frequency of $98.1 \text{ MHz}$. What is the wavelength of these radio waves?

    • $3.06 \text{ m}$
    • $0.306 \text{ m}$
    • $30.6 \text{ m}$
    • $306 \text{ m}$

    Answer: $3.06 \text{ m}$

  2. An electromagnetic wave has an electric field amplitude of $120 \text{ V/m}$. What is the amplitude of its magnetic field?

    • $4.00 \times 10^{-7} \text{ T}$
    • $3.60 \times 10^{10} \text{ T}$
    • $4.00 \times 10^{-8} \text{ T}$
    • $3.60 \times 10^{11} \text{ T}$

    Answer: $4.00 \times 10^{-7} \text{ T}$

  3. In an electromagnetic wave, how does the average energy density associated with the electric field compare to that associated with the magnetic field?

    • The electric energy density is always greater than the magnetic energy density.
    • The magnetic energy density is always greater than the electric energy density.
    • They are equal.
    • Their ratio depends on the frequency of the wave.

    Answer: They are equal.

  4. An electromagnetic wave has an average intensity of $100 \text{ W/m}^2$. What is the root-mean-square (RMS) electric field strength of this wave?

    • $194 \text{ V/m}$
    • $275 \text{ V/m}$
    • $377 \text{ V/m}$
    • $548 \text{ V/m}$

    Answer: $194 \text{ V/m}$

  5. A spacecraft is receding from Earth at a speed of $0.05c$. If it transmits a signal with a frequency of $2.0 \text{ GHz}$, what frequency would be observed on Earth?

    • $2.1 \text{ GHz}$
    • $1.9 \text{ GHz}$
    • $2.0 \text{ GHz}$
    • $1.95 \text{ GHz}$

    Answer: $1.9 \text{ GHz}$

  6. Unpolarized light with an intensity of $S_0$ passes through a polarizer. The transmitted light then passes through an analyzer whose transmission axis is at an angle of $60^\circ$ to the polarizer's transmission axis. What is the intensity of the light after passing through the analyzer?

    • $S_0$
    • $S_0/2$
    • $S_0/4$
    • $S_0/8$

    Answer: $S_0/8$

  7. The speed of light in a vacuum, $c$, is related to the permittivity of free space, $\epsilon_0$, and the permeability of free space, $\mu_0$, by the formula $c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$. This formula implies that:

    • Electromagnetic waves require a medium to propagate.
    • The speed of light is dependent on the frequency of the wave.
    • Light is an electromagnetic wave.
    • The speed of light is a fundamental constant derived from electric and magnetic properties of free space.

    Answer: The speed of light is a fundamental constant derived from electric and magnetic properties of free space.

  8. An electromagnetic wave has a frequency of $6.0 \times 10^{14} \text{ Hz}$ and an electric field amplitude of $200 \text{ V/m}$. What is the amplitude of its magnetic field?

    • $6.67 \times 10^{-7} \text{ T}$
    • $6.00 \times 10^{-7} \text{ T}$
    • $6.67 \times 10^{-8} \text{ T}$
    • $6.00 \times 10^{-8} \text{ T}$

    Answer: $6.67 \times 10^{-7} \text{ T}$

  9. A laser beam has an average intensity of $500 \text{ W/m}^2$. What is the root-mean-square (RMS) magnetic field strength of this beam?

    • $1.49 \times 10^{-6} \text{ T}$
    • $2.30 \times 10^{-6} \text{ T}$
    • $1.49 \times 10^{-7} \text{ T}$
    • $2.30 \times 10^{-7} \text{ T}$

    Answer: $1.49 \times 10^{-6} \text{ T}$

  10. A police radar gun operates at a frequency of $24 \text{ GHz}$. If it detects a car approaching at $30 \text{ m/s}$, what is the approximate change in frequency observed by the radar gun (the beat frequency)?

    • $2.4 \text{ kHz}$
    • $4.8 \text{ kHz}$
    • $48 \text{ Hz}$
    • $240 \text{ Hz}$

    Answer: $4.8 \text{ kHz}$

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