Homework Answers
Problem 1
Electromagnetic waves carry energy and momentum from one region to another in form of two mutually perpendicular waves which are electric and magnetic waves.
In empty space total energy density is given for electromagnetic waves is given by
Momentum carried is evaluated by relativistic formula
Pointing vector is associated with energy flow per unit time per unit area where as Intensity is average value of poynting vector. As momentum is transferred in an electromagnetic wave it is responsible for radiation pressure
Problem 2
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2. Describe energy and momentum in electromagnetic waves? What is Poynting vector, intensity and ...
Electromagnetic waves transport energy. This problem shows you which parts of the energy are stored in...
Electromagnetic waves transport energy. This problem shows you which parts of the energy are stored in the electric and magnetic fields, respectively, and also makes a useful connection between the energy density of a plane electromagnetic wave and the Poynting vector. In this problem, we explore the properties of a plane electromagnetic wave traveling at the speed of light c along the x axis through vacuum. Its electric and magnetic field vectors are as follows: E = E, sin (kx...
1. The electric field of an electromagnetic wave traveling through vacuum is the following: 5.90x1 :...
1. The electric field of an electromagnetic wave traveling through vacuum is the following: 5.90x1 : + a. Draw a qualitative sketch of this E function for t = 0. Add the B field as well to complete the EM wave. Be sure to label the axes. Don't worry about your drawing ability. b. What is the magnitude of the magnetic field B.? C. What is the wavelength of the EM wave? d. What is the frequency of the EM...
2. Electromagnetic waves can exert force on objects because they carry momentum. A common laser pointer...
2. Electromagnetic waves can exert force on objects because they carry momentum. A common laser pointer has a power rating of P and a cross-sectional radius of r. a. What is the intensity, I, of the laser pointer? For simplicity, we say that the energy distribution is uniform. b. What is the radiation pressure, p, if the laser pointer is aimed directly at a perfectly reflecting surface? c. What is the force, F, the laser beam exerts on a perfectly...
A plane electromagnetic wave with a time-averaged Poynting vector 〈S!〉 is incident on a long prism made from a conduc...
A plane electromagnetic wave with a time-averaged Poynting vector 〈S!〉 is incident on a long prism made from a conducting material which has a cross-section in the shape of an equilateral triangle, with side length a (see figure below). Assume that the prism is large compared to the wavelength of the electromagnetic wave and that scattering from the corners can be neglected. In other words, it can be assumed that the outgoing waves are produced by specular reflection from the...
Electromagnetic Waves 2 1 2 3 4 A plane monochromatic electromagnetic wave with wavelength 1 =...
Electromagnetic Waves 2 1 2 3 4 A plane monochromatic electromagnetic wave with wavelength 1 = 2.6 cm, propagates through a vacuum. Its magnetic field is described by B = (B,i+Byj) cos(kx + wt) where B, = 2.7 x 10-6 T, B, - 5.9 X 106T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively. 1) What is f, the frequency of this wave? 0 GHz Submit 2) What is I, the intensity of...
A light bulb emits spherical electromagnetic waves uniformly in all directions. Find (a) the intensity, (b)...
A light bulb emits spherical electromagnetic waves uniformly in all directions. Find (a) the intensity, (b) the radiation pressure, and (c) the electric and magnetic field magnitudes at a distance of 3.0 m from the light bulb, assuming that 50 W of electromagnetic radiation is emitted
The Poynting vector for an electromagnetic wave is given by (300W/m2)sin2[(1000m−1)z−(3.0×1011s−1)t]k^. Part B What is the...
The Poynting vector for an electromagnetic wave is given by (300W/m2)sin2[(1000m−1)z−(3.0×1011s−1)t]k^. Part B What is the time-averaged energy per unit time radiated through a 1.0 m2 surface aligned with its normal parallel to the direction of propagatio Part C At an instant when the electric field is in the +x direction, in what direction is the magnetic field? in the −y direction in the +y direction in the −x direction in the −z direction in the +z direction in the...
An electromagnetic wave has a frequency of 110 MHZ and is travelling in a vacuum. The...
An electromagnetic wave has a frequency of 110 MHZ and is travelling in a vacuum. The magnetic field is given by B^rightarrow (z, t) = (5.00 times 10^- 8 T) cos (Kz - omega t)i^. (Assume the electromagnetic wave is travelling in the k^direction. Find the wavelength of this wave. 2.72 m Find the electric field vector E^rightarrow (z, t). (Use the following as necessary: z, and t.) E^rightarrow (z, t) = V/m Determine the Poynting vector. (Use the following...
A neodymium-glass laser emits short pulses of high-intensity electromagnetic waves. The electric field of such a...
A neodymium-glass laser emits short pulses of high-intensity
electromagnetic waves. The electric field of such a wave has an rms
value of Erms = 2.0 × 109 N/C. Find the average power of each pulse
that passes through a 1.6 × 10-5-m2 surface that is perpendicular
to the laser beam.
A neodymium-glass laser emits short pulses of high-intensity electromagnetic waves. The electric field of such a wave has an rms value of E 2.0 x 109 NIC. Find the average...
3. A uniform plane electromagnetic wave with the time harmonic electric field intensity vector E' =ǐ10cos(cr-6m) (volts/meter) 46.μ.-Ha ) upon the is incident from the lossless medium I ( Ei 수x...
3. A uniform plane electromagnetic wave with the time harmonic electric field intensity vector E' =ǐ10cos(cr-6m) (volts/meter) 46.μ.-Ha ) upon the is incident from the lossless medium I ( Ei 수x lossless half-space medium 2 (629 Find: 4o) (a) the wave numbers and intrinsic impedances of each medium expressed in terms of air parameters ko and巩; give formulas for these air parameters. (b) the phasor reflected and transmitted electric field intensities Leave answers (c) the phasor reflected and transmitted magnetic...
Electromagnetic waves transport energy. This problem shows you which parts of the energy are stored in the electric and magnetic fields, respectively, and also makes a useful connection between the energy density of a plane electromagnetic wave and the Poynting vector. In this problem, we explore the properties of a plane electromagnetic wave traveling at the speed of light c along the x axis through vacuum. Its electric and magnetic field vectors are as follows: E = E, sin (kx...
1. The electric field of an electromagnetic wave traveling through vacuum is the following: 5.90x1 : + a. Draw a qualitative sketch of this E function for t = 0. Add the B field as well to complete the EM wave. Be sure to label the axes. Don't worry about your drawing ability. b. What is the magnitude of the magnetic field B.? C. What is the wavelength of the EM wave? d. What is the frequency of the EM...
2. Electromagnetic waves can exert force on objects because they carry momentum. A common laser pointer has a power rating of P and a cross-sectional radius of r. a. What is the intensity, I, of the laser pointer? For simplicity, we say that the energy distribution is uniform. b. What is the radiation pressure, p, if the laser pointer is aimed directly at a perfectly reflecting surface? c. What is the force, F, the laser beam exerts on a perfectly...
A plane electromagnetic wave with a time-averaged Poynting vector 〈S!〉 is incident on a long prism made from a conducting material which has a cross-section in the shape of an equilateral triangle, with side length a (see figure below). Assume that the prism is large compared to the wavelength of the electromagnetic wave and that scattering from the corners can be neglected. In other words, it can be assumed that the outgoing waves are produced by specular reflection from the...
Electromagnetic Waves 2 1 2 3 4 A plane monochromatic electromagnetic wave with wavelength 1 = 2.6 cm, propagates through a vacuum. Its magnetic field is described by B = (B,i+Byj) cos(kx + wt) where B, = 2.7 x 10-6 T, B, - 5.9 X 106T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively. 1) What is f, the frequency of this wave? 0 GHz Submit 2) What is I, the intensity of...
An electromagnetic wave has a frequency of 110 MHZ and is travelling in a vacuum. The magnetic field is given by B^rightarrow (z, t) = (5.00 times 10^- 8 T) cos (Kz - omega t)i^. (Assume the electromagnetic wave is travelling in the k^direction. Find the wavelength of this wave. 2.72 m Find the electric field vector E^rightarrow (z, t). (Use the following as necessary: z, and t.) E^rightarrow (z, t) = V/m Determine the Poynting vector. (Use the following...
A neodymium-glass laser emits short pulses of high-intensity
electromagnetic waves. The electric field of such a wave has an rms
value of Erms = 2.0 × 109 N/C. Find the average power of each pulse
that passes through a 1.6 × 10-5-m2 surface that is perpendicular
to the laser beam.
A neodymium-glass laser emits short pulses of high-intensity electromagnetic waves. The electric field of such a wave has an rms value of E 2.0 x 109 NIC. Find the average...
3. A uniform plane electromagnetic wave with the time harmonic electric field intensity vector E' =ǐ10cos(cr-6m) (volts/meter) 46.μ.-Ha ) upon the is incident from the lossless medium I ( Ei 수x lossless half-space medium 2 (629 Find: 4o) (a) the wave numbers and intrinsic impedances of each medium expressed in terms of air parameters ko and巩; give formulas for these air parameters. (b) the phasor reflected and transmitted electric field intensities Leave answers (c) the phasor reflected and transmitted magnetic...
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