Question 1

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

In an electromagnetic wave, the electric and magnetic fields are perpendicular to one another and also perpendicular to the direction of wave propagation. This can be seen in the wave equation for electromagnetic waves, where the electric field and magnetic field are both expressed as functions of position and time, but are multiplied by different constants and have different orientations. This perpendicular orientation is what allows for the propagation of the wave through space, as the electric and magnetic fields act on one another and create a self-sustaining, traveling disturbance.

Question 2

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

A

Question 3

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

E

Question 4

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

Question 5

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 in an electromagnetic wave is given by $E = cB$, where $c$ is the speed of light in vacuum (3.0 × $10^8$ m/s) and $B$ is the maximum magnetic field strength. Given $B = 1.25$ μT = $1.25 × 10^{-6}$ T, the maximum electric field $E = (3.0 × 10^8) × (1.25 × 10^{-6}) = 375$ N/C.

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 × 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. 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 7

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

Question 8

A sinusoidal electromagnetic wave in vacuum delivers energy at an average rate of 5.00 µW/m². What are the amplitudes of the electric and magnetic fields of this wave? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

Accepted Answer

The answer of A sinusoidal electromagnetic wave in vacuum delivers...

Question 9

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:
$\frac{1}{2}\epsilon_0 c E_{max}B_{max} = 0.724 W/m^2$
where $E_{max}$ and $B_{max}$ are the maximum values of the electric and magnetic fields, respectively.

Using the given values of $\epsilon_0$ and $c$, we can rearrange the equation to solve for $B_{max}$:
$B_{max} = \frac{2}{\epsilon_0 c E_{max}}(0.724 W/m^2)$

We can then use the relationship between $E_{max}$ and $B_{max}$ in an electromagnetic wave:
$E_{max} = cB_{max}/\sqrt{\mu_0\epsilon_0}$

This allows us to express $B_{max}$ solely in terms of the given values:
$B_{max} = \sqrt{\frac{\epsilon_0}{\mu_0}}\frac{0.724 W/m^2}{c} = \frac{0.724}{c}\sqrt{\frac{\epsilon_0}{\mu_0}} T$

Plugging in the values for $c$, $\epsilon_0$, and $\mu_0$, we get:
$B_{max} = \frac{0.724}{3.0	imes10^8}\sqrt{\frac{8.85	imes10^{-12}}{4\pi	imes10^{-7}}} T \approx 77.9 nT$

Therefore, the answer is (A) 77.9 nT.

Question 10

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

The answer of An electromagnetic wave propagates along the +y...

Question 11

A laser with a power of 1.0 mW has a beam radius of 1.0 mm.What is the peak value of the electric field in that beam? (c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²) A) 490 V/m B) 840 V/m C) 65 V/m D) 120 V/m E) 22 V/m

Accepted Answer

The answer of A laser with a power of 1.0...

Question 12

If the intensity of an electromagnetic wave is 80 MW/m²,what is the amplitude of the magnetic field of this wave? (c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²) A) 0.82 mT B) 0.33 µT C) 10 T D) 14 T E) 0.58 mT

Accepted Answer

The answer of If the intensity of an electromagnetic wave...

Question 13

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 the wave is given by the direction of the wave vector k, which is in the x direction (kx term). Therefore, the wave is traveling in the positive x direction.

Question 14

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 15

The magnetic field of an electromagnetic wave has a peak value of 5.0 × 10^-10 T.What is the intensity of the wave? (c = 3.0 × 10⁸ m/s,c = 3.00 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²) A) 1.0 × 10^-13 W/m² B) 1.5 × 10^-5 W/m² C) 3.0 × 10^-5 W/m² D) 2.0 × 10^-13 W/m² E) 7.5 × 10⁵ W/m²

Accepted Answer

The intensity of an electromagnetic wave is given by 
I = cε0E0^2
where c is the speed of light, ε0 is the vacuum permittivity, and E0 is the peak value of the electric field.
However, we are given the peak value of the magnetic field, B0. We know that the magnetic field and electric field are related by 
B0 = E0/c
or 
E0 = B0c
Substituting this into the expression for intensity, we get 
I = cε0(B0c)^2 = ε0cB0^2
Using the given values, we can calculate the intensity:
I = (8.85×10^-12 C^2/Nm^2)(3.00×10^8 m/s)(5.0×10^-10 T)^2
I ≈ 3.0×10^-5 W/m^2

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

Question 17

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 18

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

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

Question 19

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, according to the Poynting vector. The energy transfer between electric and magnetic fields is continuous, and they are interdependent on each other.

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 × 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 answer of Given that the wavelengths of visible light...

Quiz 30: Changing Electric Fields

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

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)

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)

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)

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 sinusoidal electromagnetic wave in vacuum delivers energy at an average rate of 5.00 µW/m². What are the amplitudes of the electric and magnetic fields of this wave? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

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)

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 laser with a power of 1.0 mW has a beam radius of 1.0 mm.What is the peak value of the electric field in that beam? (c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

If the intensity of an electromagnetic wave is 80 MW/m²,what is the amplitude of the magnetic field of this wave? (c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

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?

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

The magnetic field of an electromagnetic wave has a peak value of 5.0 × 10^-10 T.What is the intensity of the wave? (c = 3.0 × 10⁸ m/s,c = 3.00 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

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 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)

The energy per unit volume in an electromagnetic wave is

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 30: Changing Electric Fields

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

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 × 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 × 108 m/s)

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)

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 sinusoidal electromagnetic wave in vacuum delivers energy at an average rate of 5.00 µW/m2. What are the amplitudes of the electric and magnetic fields of this wave? (c = 3.0 × 108 m/s, μ0 = 4π × 10-7 T • m/A,ε0 = 8.85 × 10-12 C2/N • m2)

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)

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 laser with a power of 1.0 mW has a beam radius of 1.0 mm.What is the peak value of the electric field in that beam? (c = 3.0 × 108 m/s,μ0 = 4π × 10-7 T • m/A,ε0 = 8.85 × 10-12 C2/N • m2)

If the intensity of an electromagnetic wave is 80 MW/m2,what is the amplitude of the magnetic field of this wave? (c = 3.0 × 108 m/s,μ0 = 4π × 10-7 T • m/A,ε0 = 8.85 × 10-12 C2/N • m2)

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

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

The magnetic field of an electromagnetic wave has a peak value of 5.0 × 10-10 T.What is the intensity of the wave? (c = 3.0 × 108 m/s,c = 3.00 × 108 m/s,μ0 = 4π × 10-7 T • m/A,ε0 = 8.85 × 10-12 C2/N • m2)

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 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)

The energy per unit volume in an electromagnetic wave is

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)

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)

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)

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)

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 sinusoidal electromagnetic wave in vacuum delivers energy at an average rate of 5.00 µW/m². What are the amplitudes of the electric and magnetic fields of this wave? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

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 laser with a power of 1.0 mW has a beam radius of 1.0 mm.What is the peak value of the electric field in that beam? (c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

If the intensity of an electromagnetic wave is 80 MW/m²,what is the amplitude of the magnetic field of this wave? (c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

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 magnetic field of an electromagnetic wave has a peak value of 5.0 × 10^-10 T.What is the intensity of the wave? (c = 3.0 × 10⁸ m/s,c = 3.00 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

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)

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)