# Electromagnetic Waves

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This pack examines Maxwell's equations, electromagnetic wave production, the electromagnetic spectrum, and energy in electromagnetic waves.

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Verify that the correct value for the speed of light c is obtained when numerical values for the permeability and permittivity of free space (μ$_{0}$ and ε$_{0}$) are entered into the equation $c={1\over{\sqrt{μ_{0}ε_{0}}}}$ (answer in 10$^{8}$)

What is the maximum electric field strength in an electromagnetic wave that has a maximum magnetic field strength of 5.00×10$^{-4}$ T (about 10 times the Earth’s)?

The maximum magnetic field strength of an electromagnetic field is 5×10$^{-6}$ T. Calculate the maximum electric field strength if the wave is traveling in a medium in which the speed of the wave is 0.75c.

(a) Two microwave frequencies are authorized for use in microwave ovens: 900 and 2560 MHz. Calculate the wavelength of each. (b) Which frequency would produce smaller hot spots in foods due to interference effects?

A radio station utilizes frequencies between commercial AM and FM. What is the frequency of a 11.12-m-wavelength channel?

Combing your hair leads to excess electrons on the comb. How fast would you have to move the comb up and down to produce red light? (answer in 10$^{14}$)

Electromagnetic radiation having a 15.0−μm wavelength is classified as infrared radiation. What is its frequency? (answer in 10$^{13}$)

Approximately what is the smallest detail observable with a microscope that uses ultraviolet light of frequency 1.20×10$^{15}$ Hz? (answer in 10$^{-7}$)

A radar used to detect the presence of aircraft receives a pulse that has reflected off an object 6×10$^{-5}$ s after it was transmitted. What is the distance from the radar station to the reflecting object? (answer in 10$^{3}$)

Some radar systems detect the size and shape of objects such as aircraft and geological terrain. Approximately what is the smallest observable detail utilizing 500-MHz radar?

the Sun suddenly turned off, we would not know it until its light stopped coming. How long would that be, given that the Sun is 1.50×10$^{11}$ m away?

Conversations with astronauts on lunar walks had an echo that was used to estimate the distance to the Moon. The sound spoken by the person on Earth was transformed into a radio signal sent to the Moon, and transformed back into sound on a speaker inside the astronaut’s space suit. This sound was picked up by the microphone in the space suit (intended for the astronaut’s voice) and sent back to Earth as a radio echo of sorts. If the round-trip time was 2.60 s, what was the approximate distance to the Moon, neglecting any delays in the electronics? (answer in 10$^{8}$)

What is the intensity of an electromagnetic wave with a peak electric field strength of 125 V/m?

Find the intensity of an electromagnetic wave having a peak magnetic field strength of 4.00×10$^{-9}$ T. (answer in 10$^{-3}$)

**Integrated Concepts**
An LC circuit with a 5.00-pF capacitor oscillates in such a manner as to radiate at a wavelength of 3.30 m. (a) What is the resonant frequency? (b) What inductance is in series with the capacitor?

**Integrated Concepts**
What capacitance is needed in series with an 800−μH inductor to form a circuit that radiates a wavelength of 196 m?

**Integrated Concepts**
Police radar determines the speed of motor vehicles using the same Doppler-shift technique employed for ultrasound in medical diagnostics. Beats are produced by mixing the double Doppler-shifted echo with the original frequency. If 1.50×10$^{9}$-Hz microwaves are used and a beat frequency of 150 Hz is produced, what is the speed of the vehicle? (Assume the same Doppler-shift formulas are valid with the speed of sound replaced by the speed of light.)

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