Question 1

A 60-W light bulb emits spherical electromagnetic waves uniformly in all directions.If 50% of the power input to such a light bulb is emitted as electromagnetic radiation,what is the radiation pressure at a distance of 2.0 m from the light bulb?
A)50 nPa
B)2.0 nPa
C)8.0 nPa
D)16 nPa
E)4.0 nPa

Accepted Answer

The radiation pressure $P$ can be calculated using the formula $P = \frac{I}{c}$, where $I$ is the intensity of the wave and $c$ is the speed of light. Given that 50% of the power (60 W) is emitted as electromagnetic radiation, the effective power is 30 W. The intensity $I$ at a distance $r$ from a point source is given by $I = \frac{P}{4\pi r^2}$. Substituting the given values, $I = \frac{30}{4\pi (2)^2}$ and then calculating $P$ yields a value close to 2.0 nPa.

Question 2

You are using an antenna consisting of a single loop of wire of radius 15.0 cm to detect electromagnetic waves for which E_rms = 0.200 V/m.If the wave frequency is 600 kHz,the rms value of the emf induced in the loop is approximately A)32.1 $\mu$V B)84.3 $\mu$V C)66.7 $\mu$V D)178 $\mu$V E)643 $\mu$V

Accepted Answer

The rms value of the emf induced in the loop can be calculated using Faraday's law of electromagnetic induction, which states that the induced emf ($\epsilon$) in a loop is equal to the rate of change of magnetic flux through the loop. For a loop of radius $r$ in a uniform magnetic field that changes sinusoidally with time, the induced emf can be calculated as $\epsilon = 2\pi^2 r^2 f B_{\text{rms}}$, where $f$ is the frequency of the electromagnetic wave and $B_{\text{rms}}$ is the rms value of the magnetic field, which can be related to the electric field ($E_{\text{rms}}$) in an electromagnetic wave by $B_{\text{rms}} = E_{\text{rms}}/c$, with $c$ being the speed of light ($3 \times 10^8$ m/s).Given:- $E_{\text{rms}} = 0.200$ V/m- $r = 15.0$ cm = 0.15 m- $f = 600 \times 10^3$ HzFirst, calculate $B_{\text{rms}}$:$$B_{\text{rms}} = \frac{E_{\text{rms}}}{c} = \frac{0.200}{3 \times 10^8} \approx 6.67 \times 10^{-10} \text{T}$$Then, calculate the induced emf ($\epsilon$):$$\epsilon = 2\pi^2 (0.15)^2 (600 \times 10^3) (6.67 \times 10^{-10})$$$$\epsilon \approx 66.7 \mu V$$Therefore, the correct answer is approximately 66.7 μV, which corresponds to choice C.

Question 3

A beam of light is propagating in the x direction.The electric-field vector
A)can oscillate in any arbitrary direction in space.
B)must oscillate in the z direction.
C)must oscillate in the yz plane.
D)must oscillate in the x direction.
E)must have a steady component in the x direction.

Accepted Answer

The electric-field vector of a light beam propagating in the x direction must oscillate in the yz plane, perpendicular to the direction of propagation, due to the transverse nature of electromagnetic waves.

Question 4

Light that has a wavelength of 600 nm has a frequency of A)5.0 $\times$ 10¹⁵ Hz B)5.0 $\times$ 10¹⁴ Hz C)5.0 $\times$ 10⁶ Hz D)1.2 $\times$ 10⁵ Hz E)1.2 $\times$ 10¹⁴ Hz

Accepted Answer

The frequency of light is related to its wavelength by the equation f=c/λ, where c is the speed of light. Plugging in the given values yields: f = (3.00 x 10^8 m/s)/(600 nm x 10^-9 m/nm) = 5.0 x 10^14 Hz. Converting from scientific notation to regular notation, the frequency is 500,000,000,000,000 Hz, which can be written as 5.0 x 10^14 Hz or 5.0 x 10^10 MHz. The only choice that matches this frequency is B.

Question 5

The wavelength of a 63.7-MHz electromagnetic wave is approximately
A)1.0 m
B)4.7 m
C)6.8 m
D)7.2 cm
E)50 cm

Accepted Answer

The wavelength ($\lambda$) of an electromagnetic wave can be calculated using the formula $\lambda = \frac{c}{f}$, where $c$ is the speed of light in a vacuum ($3 \times 10^8$ m/s) and $f$ is the frequency of the wave. For a 63.7 MHz wave, $f = 63.7 \times 10^6$ Hz. Thus, $\lambda = \frac{3 \times 10^8}{63.7 \times 10^6} \approx 4.7$ meters.

Question 6

The intensity of a laser beam is 450 W/m².What is the rms value of the electric field of this laser beam? (The permittivity of free space $\varepsilon$₀ = 8.85 $\times$ 10^-12 C²/N · m² and the permeability of free space µ₀ = 4$\pi$ $\times$ 10^-7 N/A².) A)1.7 $\times$ 10⁵ V/m B)5.8 $\times$ 10² V/m C)3.4 $\times$ 10⁵ V/m D)4.1 $\times$ 10² V/m E)1.3 $\times$ 10³ V/m

Accepted Answer

The answer of The intensity of a laser beam is...

Question 7

Which of the following statements about light in a vacuum is incorrect?
A)Light always travels with the same speed c regardless of the motion of the source or observer.
B)light has wavelike properties
C)light has particlelike properties
D)Light is an electromagnetic wave with its electric-field vector pointing parallel to the direction of propagation.
E)light can be plane polarized

Accepted Answer

Light is an electromagnetic wave, but its electric-field vector oscillates perpendicular to the direction of propagation, not parallel. This perpendicular oscillation is a fundamental characteristic of electromagnetic waves, distinguishing them from longitudinal waves, where oscillation occurs in the direction of propagation.

Question 8

Electromagnetic waves that have a wavelength of 300 m in free space have a frequency of A)1 $\times$ 10^-3 Hz B)5 $\times$ 10⁵ Hz C)1 $\times$ 10⁶ Hz D)9 $\times$ 10⁶ Hz E)1 $\times$ 10¹¹ Hz

Accepted Answer

The speed of light in free space is approximately 3 x 10^8 m/s. The frequency (f) and wavelength (λ) of an electromagnetic wave are related through the equation f = c/λ, where c is the speed of light. 
Therefore, f = c/λ = (3 x 10^8 m/s)/(300 m) = 10^6 Hz = 1 x 10^16 Hz. 
The closest choice to this answer is C, which is 1 x 10^16 Hz.

Question 9

The nearest star to us,Alpha Centauri,is 4.30 light-years away.What is this distance in kilometers? A)4.1 $\times$ 10¹⁰ km B)4.1 $\times$ 10¹³ km C)4.1 $\times$ 10¹⁶ km D)6.8 $\times$ 10¹¹ km E)6.8 $\times$ 10¹⁴ km

Accepted Answer

One light-year is approximately 9.461 trillion kilometers. Multiplying this by 4.30 gives a distance close to 40.7 trillion kilometers, which is represented by the scientific notation in choice B (4.1 x 10^13 km).

Question 10

A 60-W light bulb emits spherical electromagnetic waves uniformly in all directions.If 50% of the power input to such a light bulb is emitted as electromagnetic radiation,what is the radiation intensity at a distance of 2.00 m from the light bulb? A)15 W/m² B)4.8 W/m² C)2.4 W/m² D)0.60 W/m² E)1.2 W/m²

Accepted Answer

The answer of A 60-W light bulb emits spherical electromagnetic...

Question 11

Light wave A has twice the frequency of light wave B.The wavelength of light wave A is _____ that of light wave B.
A)equal to
B)twice
C)four times
D)half
E)one-fourth

Accepted Answer

The wavelength of a wave is inversely proportional to its frequency. Therefore, if light wave A has twice the frequency of light wave B, its wavelength is halved compared to that of light wave B.

Question 12

What is the frequency of 555-nm light? A)16.7 kHz B)5.40 $\times$ 10¹⁴ Hz C)5.40 $\times$ 10¹⁵ Hz D)1.70 $\times$ 10⁷ Hz E)5.40 $\times$ 10¹⁷ Hz

Accepted Answer

The frequency of light can be calculated using the formula: frequency (f) = speed of light (c) / wavelength (λ). For 555 nm light, f = (3 x 10^8 m/s) / (555 x 10^-9 m) = 5.40 x 10^14 Hz.

Question 13

Which of the following does not result in the production of electromagnetic waves?
A)charges moving at a constant velocity
B)charges that are accelerating or decelerating
C)charges moving around in a circle
D)electrons that make a transition from one atomic level to another
E)an oscillating electric current

Accepted Answer

Electromagnetic waves are generated by accelerating charges, not by charges moving at a constant velocity. Charges that are accelerating or decelerating (B), moving in a circle (C), transitioning between atomic levels (D), or part of an oscillating electric current (E) all involve acceleration, which can produce electromagnetic waves.

Question 14

The wavelength of a 150-MHz television signal is approximately
A)1.0 m
B)1.5 m
C)2.0 m
D)2.0 cm
E)50 cm

Accepted Answer

The answer of The wavelength of a 150-MHz television signal...

Question 15

Arrange the following types of electromagnetic radiation in order of increasing wavelength: gamma rays,infrared light,ultraviolet light,visible light.
A)Gamma rays are not electromagnetic radiation.
B)gamma rays,infrared,visible,ultraviolet
C)gamma rays,ultraviolet,visible,infrared
D)visible,ultraviolet,infrared,gamma rays
E)ultraviolet,visible,infrared,gamma rays

Accepted Answer

Gamma rays have the shortest wavelength, followed by ultraviolet light, then visible light, and finally infrared light has the longest wavelength among the options given.

Question 16

The Sun radiates about 3.83 $\times$10²⁶ W of power.How large should a perfectly reflecting solar sail be on a space ship of mass 50 kg to provide an acceleration of 10^-4 m/s² at the Earth's orbit? The radius of Earth's orbit is 1.50 $\times$10¹¹ m. A)550 m² B)625 m² C)1100 m² D)2500 m² E)None of these is correct.

Accepted Answer

The correct answer is A because the power of the Sun is 3.83 x 10^26 W, the radius of the Earth's orbit is 1.50 x 10^11 m, the mass of the spaceship is 50 kg, and the acceleration is 10^-4 m/s^2. The area of the solar sail is then given by:A = P / (c * a * r)where P is the power of the Sun, c is the speed of light, a is the acceleration, and r is the radius of the Earth's orbit. Plugging in the values, we get:A = (3.83 x 10^26 W) / ((3 x 10^8 m/s) * (10^-4 m/s^2) * (1.50 x 10^11 m))= 550 m^2

Question 17

Of X rays,infrared radiation,and radio waves,which has the longest wavelength and which the shortest?
A)X rays have the longest,radio waves the shortest.
B)X rays have the longest,infrared radiation the shortest.
C)Radio waves have the longest,X rays the shortest.
D)Radio waves have the longest,infrared radiation the shortest.
E)Infrared radiation has the longest,X rays the shortest.

Accepted Answer

Radio waves have the longest wavelength in the electromagnetic spectrum, while X-rays have much shorter wavelengths.

Question 18

The frequency range for FM broadcasts is from 87.9 - 107.9 MHz in the U.S.In terms of wavelengths,the range corresponds to
A)87.9 - 107.9 m
B)2.78 - 3.41 m
C)83.3 - 102.3 m
D)12.4 - 19.5 m
E)None of these is correct.

Accepted Answer

The wavelength corresponding to a frequency range can be calculated by using the formula: wavelength = speed of light / frequency. The speed of light is approximately 3x10^8 m/s. Therefore, the wavelength range for FM broadcasts in the U.S. can be calculated as follows:

- For the lowest frequency (87.9 MHz): wavelength = 3x10^8 / 87.9x10^6 = 3.41 m
- For the highest frequency (107.9 MHz): wavelength = 3x10^8 / 107.9x10^6 = 2.78 m

Therefore, the wavelength range for FM broadcasts in the U.S. corresponds to 2.78 - 3.41 m, which is best represented by choice B).

Question 19

The detection of radio waves can be accomplished with either a dipole antenna or a loop antenna.The dipole antenna detects the _____ of the wave,and the loop antenna detects the _____ field of the wave.
A)electric field; electric
B)electric field; magnetic
C)magnetic field; magnetic
D)magnetic field; electric
E)electric and magnetic fields; electric

Accepted Answer

A dipole antenna detects the electric field of the wave, while a loop antenna detects the magnetic field of the wave.

Question 20

You are using an antenna consisting of a single loop of wire of radius 15.0 cm to detect electromagnetic waves for which E_rms = 0.200 V/m.If the wave frequency is 600 Hz,the rms value of the emf induced in the loop is approximately A)32.1 nV B)84.3 nV C)66.7 nV D)178 nV E)643 nV

Accepted Answer

The answer of You are using an antenna consisting of...

Quiz 30: Maxwells Equations and Electromagnetic Waves

A 60-W light bulb emits spherical electromagnetic waves uniformly in all directions.If 50% of the power input to such a light bulb is emitted as electromagnetic radiation,what is the radiation pressure at a distance of 2.0 m from the light bulb?

You are using an antenna consisting of a single loop of wire of radius 15.0 cm to detect electromagnetic waves for which E_rms = 0.200 V/m.If the wave frequency is 600 kHz,the rms value of the emf induced in the loop is approximately

A beam of light is propagating in the x direction.The electric-field vector

Light that has a wavelength of 600 nm has a frequency of

The wavelength of a 63.7-MHz electromagnetic wave is approximately

The intensity of a laser beam is 450 W/m².What is the rms value of the electric field of this laser beam? (The permittivity of free space $\varepsilon$ ₀ = 8.85 $\times$ 10^-12 C²/N · m² and the permeability of free space µ₀ = 4 $\pi$ $\times$ 10^-7 N/A².)

Which of the following statements about light in a vacuum is incorrect?

Electromagnetic waves that have a wavelength of 300 m in free space have a frequency of

The nearest star to us,Alpha Centauri,is 4.30 light-years away.What is this distance in kilometers?

A 60-W light bulb emits spherical electromagnetic waves uniformly in all directions.If 50% of the power input to such a light bulb is emitted as electromagnetic radiation,what is the radiation intensity at a distance of 2.00 m from the light bulb?

Light wave A has twice the frequency of light wave B.The wavelength of light wave A is _____ that of light wave B.

What is the frequency of 555-nm light?

Which of the following does not result in the production of electromagnetic waves?

The wavelength of a 150-MHz television signal is approximately

Arrange the following types of electromagnetic radiation in order of increasing wavelength: gamma rays,infrared light,ultraviolet light,visible light.

The Sun radiates about 3.83 $\times$ 10²⁶ W of power.How large should a perfectly reflecting solar sail be on a space ship of mass 50 kg to provide an acceleration of 10^-4 m/s² at the Earth's orbit? The radius of Earth's orbit is 1.50 $\times$ 10¹¹ m.

Of X rays,infrared radiation,and radio waves,which has the longest wavelength and which the shortest?

The frequency range for FM broadcasts is from 87.9 - 107.9 MHz in the U.S.In terms of wavelengths,the range corresponds to

The detection of radio waves can be accomplished with either a dipole antenna or a loop antenna.The dipole antenna detects the _ of the wave,and the loop antenna detects the _ field of the wave.

You are using an antenna consisting of a single loop of wire of radius 15.0 cm to detect electromagnetic waves for which E_rms = 0.200 V/m.If the wave frequency is 600 Hz,the rms value of the emf induced in the loop is approximately