Deck 30: Changing Electric Fields

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.

Answer 1

perpendicular to one another and perpendicular to the direction of wave propagation.

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

Answer 2

170 J

Question 3

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)

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

Answer 3

1.7 × 10^-13 T

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?

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

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

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

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)

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

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

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

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

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

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.

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

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

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.

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

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.

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

Question 21

A 7.5 × 10¹⁴ Hz laser emits a 7.7-μs pulse,5.0 mm in diameter,with a beam energy density of 0.51 J/m³. What is the amplitude of the electric field of the emitted waves? (c = 3.00 × 10⁸ m/s,
Μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

A) 340 kV/m
B) 480 kV/m
C) 240 kV/m
D) 150 kV/m
E) 120 kV/m

Question 22

A microwave oven operates with sinusoidal microwaves at a frequency of 2400 MHz.The height of the oven cavity is 25 cm and the base measures 30 cm by 30 cm.Assume that microwave energy is generated uniformly on the upper surface of the cavity and propagates directly downward toward the base.The base is lined with a material that completely absorbs microwave energy.The total microwave energy content of the cavity is 0.50 µJ.What is the intensity of the microwave beam? (c = 3.00 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

A) 5.2 kW/m²
B) 5.7 kW/m²
C) 6.2 kW/m²
D) 6.7 kW/m²
E) 7.2 kW/m²

Question 23

An 800-kHz radio signal is detected at a point 4.5 km distant from a transmitter tower.The electric field amplitude of the signal at that point is 0.63 V/m.Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed.What is the magnetic field amplitude of the signal at that point? (c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,
Ε₀ = 8.85 × 10^-12 C²/N • m²)

A) 2.1 nT
B) 1.7 nT
C) 1.3 nT
D) 2.5 nT
E) 2.9 nT

Question 24

An 800-kHz radio signal is detected at a point 2.7 km distant from a transmitter tower.The electric field amplitude of the signal at that point is 0.36 V/m.Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed.What is the intensity of the radio signal at that point? (c = 3.00 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,
Ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 170 µW/m²
B) 240 µW/m²
C) 340 µW/m²
D) 120 µW/m²
E) 86 µW/m²

Question 25

A very small source of light that radiates uniformly in all directions produces an electric field amplitude of 2.96 V/m at a point 33.0 m from the source.What is the power output from the source?
(c = 3.00 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

Question 26

A sinusoidal electromagnetic wave is propagating in vacuum.At a given point P and at a particular time,the electric field is in the +x direction and the magnetic field is in the -y direction.
(a)What is the direction of propagation of the wave?
(b)If the intensity of the wave at point P is 0.36 W/m²,what is the electric field amplitude at that point?
(c = 3.00 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

Question 27

If a beam of electromagnetic radiation has an intensity of 120 W/m²,what is the maximum value of the electric field? (c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

A) 1.5 kV/m
B) 1.0 µT
C) 1.0 µV/m
D) 0.30 kV/m
E) 0.0032 V/m

Question 28

A microwave oven operates with sinusoidal microwaves at a frequency of 2400 MHz.The height of the oven cavity is 25 cm and the base measures 30 cm by 30 cm.Assume that microwave energy is generated uniformly on the upper surface of the cavity and propagates directly downward toward the base.The base is lined with a material that completely absorbs microwave energy.The total microwave energy content of the cavity is 0.50 µJ.What is the amplitude of the electric field? (c = 3.00 × 10⁸ m/s,
Μ₀ = 4π × 10^-7 T • m/A,ε₀ = 8.85 × 10^-12 C²/N • m²)

A) 1600 V/m
B) 1900 V/m
C) 2200 V/m
D) 2500 V/m
E) 2800 V/m

Question 29

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

A) 24 kW/m²
B) 12 kW/m²
C) 8.0 kW/m²
D) 4.0 kW/m²

Question 30

Near the earth the intensity of radiation from the sun is 1.35 kW/m².What volume of space in this region contains 1.0 J of electromagnetic energy? (c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A,
Ε₀ = 8.85 × 10^-12 C²/N • m²)

A) 4.5 × 10^-6 m³
B) 3300 m³
C) 7.4 × 10^-4 m³
D) 1400 m³
E) 220,000 m³