Question 1

When an electromagnetic wave falls on a white, perfectly reflecting surface, it exerts a force F on that surface. If the surface is now painted a perfectly absorbing black, what will be the force that the same wave will exert on the surface?
A) 4F
B) 2F
C) F
D) F/2
E) F/4

Accepted Answer

When an electromagnetic wave falls on a perfectly reflecting white surface, the force it exerts on the surface is given by F=2P/c where P is the power of the wave and c is the speed of light. 
When the same wave falls on a perfectly absorbing black surface, all the energy is absorbed by the surface and none is reflected. Therefore, the force exerted on the surface is reduced by a factor of 2 due to the conservation of momentum. Thus, the force exerted on the black surface is F/2.

Question 2

A planar electromagnetic wave is propagating in the +x direction. At a certain point P and at a given instant, the electric field of the wave is given by = (0.082 V/m) ĵ. What is the magnetic vector of the wave at the point P at that instant? (c = 3.0 x 10⁸ m/s) A) 0.27 nT B) -0.27 nT C) 0.27 nT ĵ D) 6.8 nT E) -6.8 nT ĵ

Accepted Answer

A

Question 3

An electromagnetic wave propagates along the +y direction as shown in the figure. If the electric field at the origin is along the +z direction, what is the direction of the magnetic field? 
A) +z
B) -z
C) +y
D) +x
E) -x

Accepted Answer

D

Question 4

The energy per unit volume in an electromagnetic wave is
A) equally divided between the electric and magnetic fields.
B) mostly in the electric field.
C) mostly in the magnetic field.
D) all in the electric field.
E) all in the magnetic field.

Accepted Answer

The energy per unit volume in an electromagnetic wave is equally divided between the electric and magnetic fields. This is because the magnetic field is proportional to the electric field and vice versa, and they are both needed to sustain each other in the wave. Therefore, the energy is distributed evenly between the two fields.

Question 5

If the magnetic field of an electromagnetic wave is in the +x-direction and the electric field of the wave is in the +y-direction, the wave is traveling in the
A) xy-plane.
B) +z-direction.
C) -z-direction.
D) -x-direction.
E) -y-direction.

Accepted Answer

The answer of If the magnetic field of an electromagnetic...

Question 6

The magnitude of the magnetic field at point P for a certain electromagnetic wave is 2.12 μT. What is the magnitude of the electric field for that wave at P? (c = 3.0 x 10⁸ m/s) A) 636 N/C B) 745 N/C C) 5.23 µN/C D) 6.36 µN/C E) 7.45 µN/C

Accepted Answer

The relationship between the electric field (E) and the magnetic field (B) in an electromagnetic wave is given by E = cB, where c is the speed of light. Substituting the given values, E = (3.0 x 10^8 m/s)(2.12 x 10^-6 T) = 636 N/C.

Question 7

If the z-component of the magnetic field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation B_z(x, t) = (1.25 μT) cos[(3800 m^-1)x - (1.14 × 10^-12 rad/s)t], what is the largest that the y component of the electric field can be? (c = 3.0 x 10⁸ m/s) A) 375 N/C B) 4.17 × 10^-15N/C C) 3.75 × 10⁸ N/C D) 4.17 × 10^-9N/C E) 1.25 × 10⁶N/C

Accepted Answer

The maximum electric field E_max is related to the maximum magnetic field B_max by E_max = c * B_max. Given B_max = 1.25 μT = 1.25 x 10^-6 T and c = 3.0 x 10^8 m/s, E_max = 3.0 x 10^8 m/s * 1.25 x 10^-6 T = 375 N/C.

Question 8

The y component of the electric field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation E_y = (375 N/C) cos[kx - (2.20 × 10¹⁴ rad/s)t]. What is the wavelength of this electromagnetic wave? (c = 3.0 x 10⁸ m/s) A) 0.272 µm B) 1.36 µm C) 2.72 µm D) 8.57 µm E) 17.1 µm

Accepted Answer

The answer of The y component of the electric field...

Question 9

A capacitor is hooked up to a resistor and an AC voltage source as shown in the figure. The output of the source is given by V(t) = V0 sin ωt. The plates of the capacitor are disks of radius R. Point P is directly between the two plates, equidistant from them and a distance R/2 from the center axis. At point P 
A) there is no magnetic field because there is no charge moving between the plates.
B) there is a constant magnetic field.
C) there is a time-varying magnetic field.

Accepted Answer

As the AC voltage source creates a changing electric field in the capacitor, the charges on the plates of the capacitor will be alternately attracted and repelled. This movement of charges creates a time-varying current in the circuit, which in turn creates a time-varying magnetic field around the connecting wire. Therefore, at point P, there will be a time-varying magnetic field.

Question 10

Which one of the following lists is a correct representation of electromagnetic waves from longer wavelength to shorter wavelength?
A) radio waves, infrared, microwaves, UV, visible, X-rays, gamma rays
B) radio waves, UV, X-rays, microwaves, infrared, visible, gamma rays
C) radio waves, microwaves, visible, X-rays, infrared, UV, gamma rays
D) radio waves, microwaves, infrared, visible, UV, X-rays, gamma rays
E) radio waves, infrared, X-rays, microwaves, UV, visible, gamma rays

Accepted Answer

This is the correct order from longest to shortest wavelength: radio waves, microwaves, infrared, visible, UV, X-rays, gamma rays.

Question 11

The y-component of the electric field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation Ey = (375 N/C) cos[kx - (2.20 × 10¹⁴rad/s)t]. (c = 3.0 x 10⁸ m/s) (a) What is the largest that the x-component of the wave can be? (b) What is the largest that the z-component of the wave can be?

Accepted Answer

The answer of The y-component of the electric field of...

Question 12

If an electromagnetic wave has components E_y = E₀ sin(kx - ωt) and B_z = B₀ sin(kx - ωt), in what direction is it traveling? A) -x B) +x C) +y D) -y E) +z

Accepted Answer

The direction of propagation of an electromagnetic wave is given by the direction of the electric and magnetic fields. In this case, the electric field is in the y direction and the magnetic field is in the z direction. The wave is propagating in the x direction since both the electric and magnetic fields are perpendicular to the direction of propagation. Therefore, the answer is choice B, +x.

Question 13

The magnitude of the Poynting vector of a planar electromagnetic wave has an average value of 0.724 W/m². What is the maximum value of the magnetic field in the wave? (c = 3.0 x 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²) A) 77.9 nT B) 55.1 nT C) 38.9 nT D) 108 nT E) 156 nT

Accepted Answer

The average value of the Poynting vector S is related to the maximum magnetic field B_max by the equation S = (1/2) * c * ε_0 * E_max^2, where E_max = c * B_max. Solving for B_max gives B_max = sqrt(2 * S / (c * μ_0)). Substituting the given values, B_max = sqrt(2 * 0.724 / (3.0 x 10^8 * 4π x 10^-7)) = 77.9 nT.

Question 14

The magnitude of the electric field at a point P for a certain electromagnetic wave is 570 N/C. What is the magnitude of the magnetic field for that wave at P? (c = 3.0 x 10⁸ m/s) A) 2.91 µT B) 1.90 µT C) 1.10 µT D) 1.41 µT E) 2.41 µT

Accepted Answer

The answer of The magnitude of the electric field at...

Question 15

An electromagnetic wave is propagating towards the west. At a certain moment the direction of the magnetic field vector associated with this wave points vertically up. The direction of the electric field vector of this wave is
A) horizontal and pointing south.
B) vertical and pointing down.
C) horizontal and pointing north.
D) vertical and pointing up.
E) horizontal and pointing east.

Accepted Answer

The direction of the electric field vector in an electromagnetic wave is perpendicular to both the magnetic field vector and the direction of propagation. Given the magnetic field points up and the wave propagates west, using the right-hand rule, the electric field points south.

Question 16

A planar electromagnetic wave is propagating in the +x direction. At a certain point P and at a given instant, the electric field of the wave is given by = (0.082 V/m) ĵ. What is the Poynting vector at the point P at that instant? (c = 3.0 x 10⁸ m/s, μ₀= 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²) A) 18 µW/m² î B) -18 µW/m² î C) 9.0 µW/m² î D) -9.0 µW/m² î E) -18 µW/m²

Accepted Answer

The answer of A planar electromagnetic wave is propagating in...

Question 17

The magnitude of the Poynting vector of a planar electromagnetic wave has an average value of 0.939 W/m2. The wave is incident upon a rectangular area, 1.5 m by 2.0 m, at right angles. How much total electromagnetic energy falls on the area during 1.0 minute? (c = 3.0 x 10⁸ m/s, μ₀= 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²) A) 170 J B) 210 J C) 250 J D) 300 J E) 340 J

Accepted Answer

The average power of the wave is given by:$$P = \frac{1}{2} c \epsilon_0 E_0^2 A$$where:* c is the speed of light* $\epsilon_0$ is the permittivity of free space* $E_0$ is the amplitude of the electric field* A is the area of the wavefrontThe total energy falling on the area during 1.0 minute is given by:$$E = Pt = \frac{1}{2} c \epsilon_0 E_0^2 At$$where:* t is the timeSubstituting the given values, we get:$$E = \frac{1}{2} (3.0 	imes 10^8 	ext{ m/s})(8.85 	imes 10^{-12} 	ext{ C}^2/	ext{N} \cdot 	ext{m}^2)(0.939 	ext{ W/m}^2)(1.5 	ext{ m})(2.0 	ext{ m})(60 	ext{ s})$$$$E = 170 	ext{ J}$$Therefore, the correct answer is A.

Question 18

If the electric field and magnetic field of an electromagnetic wave are given by E = E₀ sin(kx - ωt) and B = B₀ sin(kx - ωt), and if the value of E0 is 51 µV/m, what is the value of B₀? (c = 3.0 x 10⁸ m/s) A) 1.7 × 10¹⁴ T B) 1.7 × 10³ T C) 1.7 × 10^-14 T D) 1.7 × 10⁴T E) 1.7 × 10^-13 T

Accepted Answer

The relationship between the electric field (E) and magnetic field (B) in an electromagnetic wave is given by E = cB, where c is the speed of light. Solving for B gives B = E/c. Substituting E0 = 51 µV/m and c = 3.0 x 10^8 m/s, we find B0 = 51 x 10^-6 V/m / 3.0 x 10^8 m/s = 1.7 x 10^-13 T.

Question 19

In an electromagnetic wave, the electric and magnetic fields are oriented such that they are
A) parallel to one another and perpendicular to the direction of wave propagation.
B) parallel to one another and parallel to the direction of wave propagation.
C) perpendicular to one another and perpendicular to the direction of wave propagation.
D) perpendicular to one another and parallel to the direction of wave propagation.

Accepted Answer

Electromagnetic waves consist of oscillating electric and magnetic fields perpendicular to one another and perpendicular to the direction of wave propagation. This is known as transverse wave nature. Therefore, option C is the correct choice.

Question 20

Given that the wavelengths of visible light range from 400 nm to 700 nm, what is the highest frequency of visible light? (c = 3.0 x 10⁸ m/s) A) 3.1 × 10⁸ Hz B) 7.5 × 10¹⁴ Hz C) 2.3 × 10²⁰ Hz D) 4.3 × 10¹⁴ Hz E) 5.0 × 10⁸ Hz

Accepted Answer

The highest frequency corresponds to the shortest wavelength. Using the formula $ f = \frac{c}{\lambda} $, where $ c = 3.0 \times 10^8 $ m/s and $ \lambda = 400 $ nm = $ 400 \times 10^{-9} $ m, the frequency is $ 7.5 \times 10^{14} $ Hz.

Quiz 31: Electromagnetic Waves

When an electromagnetic wave falls on a white, perfectly reflecting surface, it exerts a force F on that surface. If the surface is now painted a perfectly absorbing black, what will be the force that the same wave will exert on the surface?

A planar electromagnetic wave is propagating in the +x direction. At a certain point P and at a given instant, the electric field of the wave is given by = (0.082 V/m) ĵ. What is the magnetic vector of the wave at the point P at that instant? (c = 3.0 x 10⁸ m/s)

An electromagnetic wave propagates along the +y direction as shown in the figure. If the electric field at the origin is along the +z direction, what is the direction of the magnetic field?

The energy per unit volume in an electromagnetic wave is

If the magnetic field of an electromagnetic wave is in the +x-direction and the electric field of the wave is in the +y-direction, the wave is traveling in the

The magnitude of the magnetic field at point P for a certain electromagnetic wave is 2.12 μT. What is the magnitude of the electric field for that wave at P? (c = 3.0 x 10⁸ m/s)

If the z-component of the magnetic field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation B_z(x, t) = (1.25 μT) cos[(3800 m^-1) x - (1.14 × 10^-12 rad/s) t], what is the largest that the y component of the electric field can be? (c = 3.0 x 10⁸ m/s)

The y component of the electric field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation E_y = (375 N/C) cos[kx - (2.20 × 10¹⁴ rad/s) t]. What is the wavelength of this electromagnetic wave? (c = 3.0 x 10⁸ m/s)

Which one of the following lists is a correct representation of electromagnetic waves from longer wavelength to shorter wavelength?

If an electromagnetic wave has components E_y = E₀ sin(kx - ωt) and B_z = B₀ sin(kx - ωt) , in what direction is it traveling?

The magnitude of the Poynting vector of a planar electromagnetic wave has an average value of 0.724 W/m². What is the maximum value of the magnetic field in the wave? (c = 3.0 x 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

The magnitude of the electric field at a point P for a certain electromagnetic wave is 570 N/C. What is the magnitude of the magnetic field for that wave at P? (c = 3.0 x 10⁸ m/s)

An electromagnetic wave is propagating towards the west. At a certain moment the direction of the magnetic field vector associated with this wave points vertically up. The direction of the electric field vector of this wave is

If the electric field and magnetic field of an electromagnetic wave are given by E = E₀ sin(kx - ωt) and B = B₀ sin(kx - ωt) , and if the value of E0 is 51 µV/m, what is the value of B₀? (c = 3.0 x 10⁸ m/s)

In an electromagnetic wave, the electric and magnetic fields are oriented such that they are

Given that the wavelengths of visible light range from 400 nm to 700 nm, what is the highest frequency of visible light? (c = 3.0 x 10⁸ m/s)

Quiz 31: Electromagnetic Waves

When an electromagnetic wave falls on a white, perfectly reflecting surface, it exerts a force F on that surface. If the surface is now painted a perfectly absorbing black, what will be the force that the same wave will exert on the surface?

A planar electromagnetic wave is propagating in the +x direction. At a certain point P and at a given instant, the electric field of the wave is given by = (0.082 V/m) ĵ. What is the magnetic vector of the wave at the point P at that instant? (c = 3.0 x 108 m/s)

An electromagnetic wave propagates along the +y direction as shown in the figure. If the electric field at the origin is along the +z direction, what is the direction of the magnetic field?

The energy per unit volume in an electromagnetic wave is

If the magnetic field of an electromagnetic wave is in the +x-direction and the electric field of the wave is in the +y-direction, the wave is traveling in the

The magnitude of the magnetic field at point P for a certain electromagnetic wave is 2.12 μT. What is the magnitude of the electric field for that wave at P? (c = 3.0 x 108 m/s)

If the z-component of the magnetic field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation Bz(x, t) = (1.25 μT) cos[(3800 m-1) x - (1.14 × 10-12 rad/s) t], what is the largest that the y component of the electric field can be? (c = 3.0 x 108 m/s)

The y component of the electric field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation Ey = (375 N/C) cos[kx - (2.20 × 1014 rad/s) t]. What is the wavelength of this electromagnetic wave? (c = 3.0 x 108 m/s)