CAPA 10 winter 2014 MOORE
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
1
Notes: 1. To submit a problem, just click the ”Submit” button under it.
The ”Submit All” button is not necessary. 2. A problem accepted as correct by CAPA will be highlighted in green. Once you see this, your problem has been submitted and accepted as correct.
3. If you are trying to obtain the correct number of significant digits, use the ’E’ notation. I.e. 44+56 = 100. is wrong, but 45 + 56 = 1.0e2 is right in the number of significant digits. 4. Use period ”.” to denote decimal point. comma ”,” doesn’t work here.
5. You are encouraged to solve all the problems independently. For questions about the assignment itself, please consult one of your tutors. If you have any questions about the capa system, don’t hesitate to contact [email protected], i’ll be glad to help you.
Good Luck!
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
2
The intensity of solar radiation at the top of the Earth’s atmosphere is 1340 W/m2. Assuming that 59.5% of the incoming solar energy reaches the Earth’s surface and assuming that you absorb 50.9% of the incident energy, estimate the amount of solar energy you absorb in a 70.0 minutes sunbath, assuming that you cover a 1.65 m by 0.258 m section of beach blanket and the elevation angle of the Sun is 56.4◦ . You are correct. Your receipt is 151-3084 Problem 3
A 1.33 m diameter mirror focuses the Sun’s rays onto an absorbing plate 2.16 cm in radius, which holds a can containing 1.49 L of water at 20.0 ◦ C. If the solar intensity is 1.06 kW/m2: a) What is the intensity on the absorbing plate? You are correct. Your receipt is 151-8413
b) What is the maximum magnitude of the field E? Problem 1
You are correct. Your receipt is 151-7558
A plane electromagnetic wave has an intensity of 762 W/m2. A flat rectangular surface of dimensions 54.9 cm x 110 cm is placed perpendicular to the direction of the wave. If the surface absorbs half of the energy and reflects half:
c) What is the maximum magnitude of the field B?
a) Calculate the total energy absorbed by the surface in 2.00 minutes.
d) If 38.2% of the energy is absorbed, how long would it take to bring the water to its boiling point? (it takes 4.18 J of energy to raise 1 g of water 1°C. )
You are correct. Your receipt is 151-2927
You are correct. Your receipt is 151-9465 You are correct. Your receipt is 151-8961 b) Calculate the momentum absorbed in this time. You are correct. Your receipt is 151-1376 Problem 2
Problem 4
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
3
A microwave source produces pulses of 19.5 GHz radiation, with each pulse lasting 1.33 ns. A parabolic reflector (R = 6.10 cm, D = 12.2 cm) is used to focus these pulses into a parallel beam of radiation, as shown in the figure below.
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
4
A beam of light, of intensity I= 365 W/m2 , travels in the x direction. It is polarized so the electric field is in the z direction.
a) It passes through an ideal polarizer (which allows all light in the correct polarization and blocks all light in the wrong polarization), oriented to allow through the electric field in the y direction. What is the transmitted intensity? You are correct. Your receipt is 151-1006
The average power during each pulse is 24.2 kW.
b) Suppose an ideal polarizer is inserted before the beam reaches the y-polarizer. The inserted polarizer is oriented 45° from the z axis. Now what light intensity emerges from the y-polarizer?
a) What is the wavelength of these microwaves?
You are correct. Your receipt is 151-6959
b) What is the total energy contained in each pulse?
c) Now suppose that two polarizers are inserted; the first has an angle of 30° from the z-axis, the second has an angle of 60° from the z-axis. Now what light intensity emerges from the y-polarizer?
You are correct. Your receipt is 151-72
You are correct. Your receipt is 151-7763
c) Compute the average energy density inside each pulse.
d) Now insert five polarizers, with angles 15, 30, 45, 60, and 75° from the z-axis. How much light intensity makes it through the (six total) polarizers?
You are correct. Your receipt is 151-5455
You are correct. Your receipt is 151-6764
You are correct. Your receipt is 151-5267
d) Determine the amplitude of the electric field in these microwaves.
e) Suppose you use 17 polarizers, with angles 5, 10, ..., 85°?
You are correct. Your receipt is 151-5600
You are correct. Your receipt is 151-261 (nb: In the real world the polarizers would each absorb some of the light. There are better ways of rotating the polarization with little loss, such as a quarter-wave plate.)
e) Determine the amplitude of the magnetic field in these microwaves. You are correct. Your receipt is 151-6206 Problem 5
Problem 6
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
5
The Sun’s mass is M1 = \ensuremath{1.99\times 10ˆ{30}} kg and it is r = 153 million km away. At this distance the light from the Sun has an intensity of I = 1360. W/m2 . The Earth’s mass is M2 = \ensuremath{5.97\times 10ˆ{24}} kg and its radius is 6370 km.
a)What is the gravitational force on the Earth from the Sun, in Newtons? You are correct. Your receipt is 151-5405 b) What is the force on the Earth due to the Sun’s radiation pressure? You are correct. Your receipt is 151-1947 c) A solar sail is a very thin piece of material, thin enough that the Sun’s radiation pressure can balance or exceed the Sun’s gravitational force. Suppose a solar sail has an area of A = \ensuremath{3.00\times 10ˆ{4}} m2 , a density of ρ = \ensuremath{2.10\times 10ˆ{3}} kg/m3 and a thickness of t = \ensuremath{1.50\times 10ˆ{-4}} m. Its distance from the Sun is the same as the Earth’s and it is turned to meet the Sun’s rays at normal incidence. What is the force on the sail due to radiation pressure? (Assume the light is absorbed.) You are correct. Your receipt is 151-2008 d) What is the force from gravity? You are correct. Your receipt is 151-6801 e) How thin would the thickness, t, need to be for these to equal? You are correct. Your receipt is 151-6214 Problem Set End. You do not need to hit the ”Submit All” button below this line if you have already clicked ”submit” for each individual field.
c Printed from LON-CAPA MSU
Licensed under GNU General Public License
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
6
1
Notes: 1. To submit a problem, just click the ”Submit” button under it.
The ”Submit All” button is not necessary. 2. A problem accepted as correct by CAPA will be highlighted in green. Once you see this, your problem has been submitted and accepted as correct.
3. If you are trying to obtain the correct number of significant digits, use the ’E’ notation. I.e. 44+56 = 100. is wrong, but 45 + 56 = 1.0e2 is right in the number of significant digits. 4. Use period ”.” to denote decimal point. comma ”,” doesn’t work here.
5. You are encouraged to solve all the problems independently. For questions about the assignment itself, please consult one of your tutors. If you have any questions about the capa system, don’t hesitate to contact [email protected], i’ll be glad to help you.
Good Luck!
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
2
The intensity of solar radiation at the top of the Earth’s atmosphere is 1340 W/m2. Assuming that 59.5% of the incoming solar energy reaches the Earth’s surface and assuming that you absorb 50.9% of the incident energy, estimate the amount of solar energy you absorb in a 70.0 minutes sunbath, assuming that you cover a 1.65 m by 0.258 m section of beach blanket and the elevation angle of the Sun is 56.4◦ . You are correct. Your receipt is 151-3084 Problem 3
A 1.33 m diameter mirror focuses the Sun’s rays onto an absorbing plate 2.16 cm in radius, which holds a can containing 1.49 L of water at 20.0 ◦ C. If the solar intensity is 1.06 kW/m2: a) What is the intensity on the absorbing plate? You are correct. Your receipt is 151-8413
b) What is the maximum magnitude of the field E? Problem 1
You are correct. Your receipt is 151-7558
A plane electromagnetic wave has an intensity of 762 W/m2. A flat rectangular surface of dimensions 54.9 cm x 110 cm is placed perpendicular to the direction of the wave. If the surface absorbs half of the energy and reflects half:
c) What is the maximum magnitude of the field B?
a) Calculate the total energy absorbed by the surface in 2.00 minutes.
d) If 38.2% of the energy is absorbed, how long would it take to bring the water to its boiling point? (it takes 4.18 J of energy to raise 1 g of water 1°C. )
You are correct. Your receipt is 151-2927
You are correct. Your receipt is 151-9465 You are correct. Your receipt is 151-8961 b) Calculate the momentum absorbed in this time. You are correct. Your receipt is 151-1376 Problem 2
Problem 4
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
3
A microwave source produces pulses of 19.5 GHz radiation, with each pulse lasting 1.33 ns. A parabolic reflector (R = 6.10 cm, D = 12.2 cm) is used to focus these pulses into a parallel beam of radiation, as shown in the figure below.
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
4
A beam of light, of intensity I= 365 W/m2 , travels in the x direction. It is polarized so the electric field is in the z direction.
a) It passes through an ideal polarizer (which allows all light in the correct polarization and blocks all light in the wrong polarization), oriented to allow through the electric field in the y direction. What is the transmitted intensity? You are correct. Your receipt is 151-1006
The average power during each pulse is 24.2 kW.
b) Suppose an ideal polarizer is inserted before the beam reaches the y-polarizer. The inserted polarizer is oriented 45° from the z axis. Now what light intensity emerges from the y-polarizer?
a) What is the wavelength of these microwaves?
You are correct. Your receipt is 151-6959
b) What is the total energy contained in each pulse?
c) Now suppose that two polarizers are inserted; the first has an angle of 30° from the z-axis, the second has an angle of 60° from the z-axis. Now what light intensity emerges from the y-polarizer?
You are correct. Your receipt is 151-72
You are correct. Your receipt is 151-7763
c) Compute the average energy density inside each pulse.
d) Now insert five polarizers, with angles 15, 30, 45, 60, and 75° from the z-axis. How much light intensity makes it through the (six total) polarizers?
You are correct. Your receipt is 151-5455
You are correct. Your receipt is 151-6764
You are correct. Your receipt is 151-5267
d) Determine the amplitude of the electric field in these microwaves.
e) Suppose you use 17 polarizers, with angles 5, 10, ..., 85°?
You are correct. Your receipt is 151-5600
You are correct. Your receipt is 151-261 (nb: In the real world the polarizers would each absorb some of the light. There are better ways of rotating the polarization with little loss, such as a quarter-wave plate.)
e) Determine the amplitude of the magnetic field in these microwaves. You are correct. Your receipt is 151-6206 Problem 5
Problem 6
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
5
The Sun’s mass is M1 = \ensuremath{1.99\times 10ˆ{30}} kg and it is r = 153 million km away. At this distance the light from the Sun has an intensity of I = 1360. W/m2 . The Earth’s mass is M2 = \ensuremath{5.97\times 10ˆ{24}} kg and its radius is 6370 km.
a)What is the gravitational force on the Earth from the Sun, in Newtons? You are correct. Your receipt is 151-5405 b) What is the force on the Earth due to the Sun’s radiation pressure? You are correct. Your receipt is 151-1947 c) A solar sail is a very thin piece of material, thin enough that the Sun’s radiation pressure can balance or exceed the Sun’s gravitational force. Suppose a solar sail has an area of A = \ensuremath{3.00\times 10ˆ{4}} m2 , a density of ρ = \ensuremath{2.10\times 10ˆ{3}} kg/m3 and a thickness of t = \ensuremath{1.50\times 10ˆ{-4}} m. Its distance from the Sun is the same as the Earth’s and it is turned to meet the Sun’s rays at normal incidence. What is the force on the sail due to radiation pressure? (Assume the light is absorbed.) You are correct. Your receipt is 151-2008 d) What is the force from gravity? You are correct. Your receipt is 151-6801 e) How thin would the thickness, t, need to be for these to equal? You are correct. Your receipt is 151-6214 Problem Set End. You do not need to hit the ”Submit All” button below this line if you have already clicked ”submit” for each individual field.
c Printed from LON-CAPA MSU
Licensed under GNU General Public License
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
6
