Question 1

Electromagnetic waves: 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) . What is the magnetic vector of the wave at the point P at that instant? (c = 3.0 × 10⁸ m/s) A) 0.27 nT B) -0.27 nT C) 0.27 nT D) 6.8 nT E) -6.8 nT

Accepted Answer

A

Question 2

Displacement current: 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

According to Ampere's law, a magnetic field can be produced by a time-varying electric field. In this case, as the AC voltage source is providing a time-varying electric field across the plates of the capacitor, a displacement current will flow between the plates, producing a time-varying magnetic field around point P. Therefore, choice C is correct. Choice A is incorrect because even though charge does not move between the plates, displacement current still flows, producing a magnetic field. Choice B is incorrect because the magnetic field is not constant, but rather varies with time due to the time-varying electric field.

Question 3

Electromagnetic waves: 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 components of the electromagnetic wave involve the sin function with only kx - ωt, indicating that the wave is traveling in the x-direction. Therefore, the correct answer is +x.

Question 4

Poynting vector: 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) . What is the Poynting vector at the point P at that instant? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10-7 T ∙· m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²) A) 18 µW/m² B) -18 µW/m² C) 9.0 µW/m² D) -9.0 µW/m² E) -18 µW/m²

Accepted Answer

The Poynting vector can be calculated using the formula S = (1/μ) E x B, where E is the electric field and B is the magnetic field. However, since the problem only provides information about the electric field, we need to use the fact that the wave is propagating in the +x direction to determine the direction of the magnetic field. This can be done using the right-hand rule, which dictates that the magnetic field will be in the +z direction. Therefore, B = (0,0,Bz), where Bz is the magnitude of the magnetic field. Using the fact that the wave is electromagnetic, we can relate Bz to the magnitude of the electric field using the equation Bz = E/c, where c is the speed of light. Substituting these values into the formula for the Poynting vector yields S = (1/μ) E x B = (1/μ) (0.082 V/m) (0,0,E/c) x (0,0,Bz) = (1/μ) (0.082 V/m) (-E/c,0,0) x (0,0,E/c) = (1/μ) (0.082 V/m) (0,-E/c,0) = (0,-E2/μc,0). Finally, we can substitute the values of μ and c to obtain S = (0,-E2/μc,0) = (0,-(0.082 V/m)2/(4π × 10-7 T ∙· m/A)(3.0 × 10S1U1P8S1S1P m/s),0) = (0,-18 µW/m²,0). Therefore, the answer is (A).

Question 5

Electromagnetic waves: 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

In an electromagnetic wave, the energy per unit volume is equally divided between the electric and magnetic fields. This is known as the Poynting vector, which describes the direction and magnitude of energy flow in an electromagnetic wave.

Question 6

Electromagnetic waves: If the electric field and magnetic field of an electromagnetic wave are given by E = E₀sin(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 × 10⁸ m/s) A) 1.7 × 10¹⁴ T B) 1.7 × 10³ T C) 1.7 × 10^-14 T D) 1.7 × 10⁴ T 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 = 51 × 10^-6 V/m / 3.0 × 10^8 m/s = 1.7 × 10^-13 T.

Question 7

Poynting vector: 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 × 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:$$P_{avg} = \frac{1}{2}c\epsilon_0 E_0^2$$where c is the speed of light, $\epsilon_0$ is the permittivity of free space, and $E_0$ is the amplitude of the electric field.The total energy falling on the area during 1.0 minute is given by:$$E = P_{avg}At$$where A is the area of the rectangle and t is the time.Substituting 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 8

Electromagnetic waves: 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 × 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 magnitude of the electric field (E) in an electromagnetic wave is related to the magnitude of the magnetic field (B) by the equation E = cB, where c is the speed of light (3.0 × 10^8 m/s). Substituting the given values, E = (3.0 × 10^8 m/s)(2.12 μT) = (3.0 × 10^8 m/s)(2.12 × 10^-6 T) = 636 N/C.

Question 9

Electromagnetic waves: 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 Electromagnetic waves: If the magnetic field of...

Question 10

Electromagnetic waves: 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]. (c = 3.0 × 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 Electromagnetic waves: The y-component of the electric...

Question 11

Electromagnetic waves: 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

Electromagnetic waves follow the right-hand rule, where the thumb points in the direction of propagation, the fingers point in the direction of the electric field, and the palm faces in the direction of the magnetic field. If the wave is moving west and the magnetic field is up, the electric field must be pointing south.

Question 12

Electromagnetic waves: 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 × 10⁸ m/s) A) 375 N/C B) 4.17 × 10^-15 N/C C) 3.75 × 10⁸ N/C D) 4.17 × 10^-9 N/C E) 1.25 × 10⁶ N/C

Accepted Answer

The largest value of the y-component of the electric field can be found using the relationship between the electric and magnetic fields in an electromagnetic wave, which is $E = cB$. Given $B = 1.25 \mu T = 1.25 \times 10^{-6} T$ and $c = 3.0 \times 10^8 m/s$, the maximum electric field $E = (3.0 \times 10^8 m/s) \times (1.25 \times 10^{-6} T) = 375 N/C$.

Question 13

Radiation pressure: 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 surface, the force it exerts is twice the radiation pressure (F = 2P/c, where P is the radiation pressure and c is the speed of light).

So, if the force exerted on a white, perfectly reflecting surface is F, the force exerted on a perfectly absorbing black surface will be half of F, or F/2.

Question 14

Electromagnetic waves: 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 perpendicular electric and magnetic fields that are both perpendicular to the direction of wave propagation. This is known as transverse polarization.

Question 15

Electromagnetic waves: 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 list is in order from longer wavelengths to shorter wavelengths. Radio waves have the longest wavelengths and gamma rays have the shortest wavelengths.

Question 16

Poynting vector: 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 × 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 is given by:$$S_{avg} = \frac{1}{2}ε_0 c E_0^2$$where:* S_avg is the average value of the Poynting vector* ε_0 is the permittivity of free space* c is the speed of light* E_0 is the amplitude of the electric fieldThe maximum value of the magnetic field is given by:$$B_0 = \frac{E_0}{c}$$where:* B_0 is the maximum value of the magnetic fieldSubstituting the given values into the above equations, we get:$$S_{avg} = \frac{1}{2}(8.85 × 10^{-12} C^2/N \cdot m^2)(3.0 × 10^8 m/s)(E_0^2)$$$$B_0 = \frac{E_0}{3.0 × 10^8 m/s}$$Solving for E_0, we get:$$E_0 = \sqrt{\frac{2S_{avg}}{ε_0 c}} = \sqrt{\frac{2(0.724 W/m^2)}{8.85 × 10^{-12} C^2/N \cdot m^2(3.0 × 10^8 m/s)}} = 2.45 × 10^3 V/m$$Substituting this value into the equation for B_0, we get:$$B_0 = \frac{2.45 × 10^3 V/m}{3.0 × 10^8 m/s} = 77.9 nT$$Therefore, the correct answer is A.

Question 17

Electromagnetic waves: 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

According to the right-hand rule, the magnetic field would be in the +x direction. The direction of the electric field determines the orientation of the wave, while the magnetic field is perpendicular to both the electric field and the direction of propagation.

Question 18

Electromagnetic waves: 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 × 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 magnitude of the electric field (E) and the magnitude of the magnetic field (B) in an electromagnetic wave are related by the equation:

E/B = c

where c is the speed of light.

Therefore,

B = E/c = 570 N/C / 3.0 × 10^8 m/s = 1.90 µT

Thus, the answer is B.

Question 19

Electromagnetic waves: 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 × 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 Electromagnetic waves: The y component of the...

Question 20

Electromagnetic waves: 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 × 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

We know that the speed of electromagnetic waves (c) is equal to the product of their wavelength (λ) and frequency (f):

c = λf

Rearranging this formula, we get:

f = c/λ

For the highest frequency of visible light, we need to find the shortest wavelength (which corresponds to blue/violet light). Using λ = 400 nm, we get:

f = (3.0 × 10^8 m/s) / (400 × 10^-9 m) = 7.5 × 10^14 Hz

This matches answer choice B.

Quiz 26: Direct-Current Circuits

Electromagnetic waves: 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) . What is the magnetic vector of the wave at the point P at that instant? (c = 3.0 × 10⁸ m/s)

Electromagnetic waves: 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?

Electromagnetic waves: The energy per unit volume in an electromagnetic wave is

Electromagnetic waves: If the electric field and magnetic field of an electromagnetic wave are given by E = E₀sin(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 × 10⁸ m/s)

Electromagnetic waves: 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 × 10⁸ m/s)

Electromagnetic waves: 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

Electromagnetic waves: 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

Radiation pressure: 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?

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

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

Poynting vector: 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 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Electromagnetic waves: 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?

Electromagnetic waves: 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 × 10⁸ m/s)

Electromagnetic waves: 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 × 10⁸ m/s)

Electromagnetic waves: 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 × 10⁸ m/s)

Quiz 26: Direct-Current Circuits

Electromagnetic waves: 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) . What is the magnetic vector of the wave at the point P at that instant? (c = 3.0 × 108 m/s)

Electromagnetic waves: If an electromagnetic wave has components Ey = E0 sin(kx - ωt) and Bz = B0 sin(kx - ωt) , in what direction is it traveling?