A Microwave's Magnetic Field

Q. In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 × 10¹⁰ Hz and amplitude 48 V/m. What is the amplitude of the oscillating magnetic field, in teslas? expects 1.6 × 10⁻⁷ T

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Q. In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 × 10¹⁰ Hz and amplitude 48 V/m $E = 48$ V/m. What is the amplitude of the oscillating magnetic field, in teslas?

The playground

Inputs

electric

E

48 V/m

Outputs

magnetic

B

The solution

Solved with ElectromagneticWave

Given

$E = 48$ V/m

Find $B$ .

Working

fields of a light wave(wave) $E = c \cdot B$
$48 = 2.99792458 \times 10^{8} \cdot B$
$B = 1.601 \times 10^{−7}$ T
$B \approx 1.6 \times 10^{−7}$ Tto 2 significant figures

Conclusion

The magnetic field of a light wave is its electric field over the speed of light, whatever the frequency.

The Ruby

1require_relative "../physics"23question :a_microwave_s_magnetic_field do4  kind :numerical5  describes "In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 × " \6            "10¹⁰ Hz and amplitude %{electric}. %{magnetic}, in teslas?"7  given electric: "48 V/m"8  asks magnetic: "What is the amplitude of the oscillating magnetic field"9end

1require_relative "../questions/a_microwave_s_magnetic_field"2require_relative "../science/electromagnetic_waves/electromagnetic_wave"34solve :a_microwave_s_magnetic_field, using: ElectromagneticWave do5  objects :wave67  take electric: wave.electric_field89  magnetic = wave.magnetic_field10  answer magnetic:, in: "T", figures: 21112  conclusion "The magnetic field of a light wave is its electric field over the speed of light, whatever the " \13             "frequency."14end

1require_relative "../solutions/a_microwave_s_magnetic_field"23play_with :a_microwave_s_magnetic_field do4  title "A Microwave's Magnetic Field"5end

The laws

quantity	written	units	within	from
pi	$π$	—	0 … ∞	ElectromagneticWave
speed of light	$c$	m/s	—	ElectromagneticWave
electric field	$E$	V/m	—	ElectromagneticWave
magnetic field	$B$	T	—	ElectromagneticWave
wave number	$k$	m⁻¹	—	ElectromagneticWave
angular frequency	$ω$	rad/s	—	ElectromagneticWave
wavelength	$λ$	m	0 … ∞	ElectromagneticWave
frequency	$ν$	Hz	0 … ∞	ElectromagneticWave
electric field of ground	$E_{g}$	V/m	—
magnetic field of ground	$B_{g}$	T	—
electric field of wave	$E$	V/m	—
magnetic field of wave	$B$	T	—
wave number of ground	$k_{g}$	m⁻¹	—
wavelength of ground	$λ_{g}$	m	0 … ∞
wave number of wave	$k$	m⁻¹	—
wavelength of wave	$λ$	m	0 … ∞
angular frequency of ground	$ω_{g}$	rad/s	—
frequency of ground	$ν_{g}$	Hz	0 … ∞
angular frequency of wave	$ω$	rad/s	—
frequency of wave	$ν$	Hz	0 … ∞

E_{w} = c \cdot B_{w}

fields of a light wave

k_{w} = \frac{2 \cdot π}{λ_{w}}

wave number and wavelength

ω_{w} = 2 \cdot π \cdot ν_{w}

angular frequency and frequency

c = ν_{w} \cdot λ_{w}

light travels at c

E_{g} = c \cdot B_{g}

fields of a light wave(ground)

E = c \cdot B

fields of a light wave(wave)

k_{g} = \frac{2 \cdot π}{λ_{g}}

wave number and wavelength(ground)

k = \frac{2 \cdot π}{λ}

wave number and wavelength(wave)

ω_{g} = 2 \cdot π \cdot ν_{g}

angular frequency and frequency(ground)

ω = 2 \cdot π \cdot ν

angular frequency and frequency(wave)

c = ν_{g} \cdot λ_{g}

light travels at c(ground)

c = ν \cdot λ

light travels at c(wave)