CAPA 4 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!
Problem 1 A parallel-plate air capacitor of area A = 26.0 cm2 and plate separation d = 2.00 mm is charged by a battery to a voltage 60.0 V. If a dielectric material with κ =5.00 is inserted so that it fills the volume between the plates (with the capacitor still connected to the battery), how much additional charge will flow from the battery onto the positive plate?
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
The Earth is a conducting sphere of radius R = 6370 km. At the Earth’s surface there is an electric field, pointing downward, of magnitude E(R) = 230.0 V/m. a) What is the total charge of the Earth? You are correct. Your receipt is 151-2992 b) Assume that there are no other charges in the Earth’s atmosphere, etc. (Actually there are – but for this problem pretend that there are not.) What is the voltage at the surface of the Earth, if we take the voltage very far from the Earth to be 0 Volts? (Take the dielectric constant of air to be 1.) You are correct. Your receipt is 151-6190 c) Based on these two results, what is the capacitance of the Earth? You are correct. Your receipt is 151-8932 d) Find an expression for the energy density, u(r), in the electric field at a distance r > R, from the centre of the Earth. What is the electric field energy density at r = 13500 km? You are correct. Your receipt is 151-8931 e) Integrate R ∞ your expression for the energy density over all space, R u(r)4πr2 dr. What is the total energy stored in the electric field? You are correct. Your receipt is 151-9218 f) Is your answer above the same as the expression for energy stored in a capacitor, Q2 /(2C)? Choices: Yes, No. You are correct. Your receipt is 151-5536
Problem Weight is: 1 Problem 3 You are correct. Your receipt is 151-8069 Problem 2
2
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
3
a) What is the equivalent capacitance of the four identical capacitors between terminals A and B if C1 = C2 = C3 = C4 = 87.0 µF ? (Give your answer in uF)
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
4
a) Two capacitors (C1 = 6.00 µF, C2 = 19.3 µF) are charged individually to (V1 = 13.7 V, V2 = 5.80 V). The two capacitors are then connected together in parallel with the positive plates together and the negative plates together. Calculate the final potential difference across the plates of the capacitors once they are connected. Problem Weight is: 1 You are correct. Your receipt is 151-1539 b) Calculate the amount of charge that flows from one capacitor to the other when the capacitors are connected together. Problem Weight is: 1 You are correct. Your receipt is 151-5745 c) By how much is the total stored energy reduced when the two capacitors are connected? Problem Weight is: 1
Problem Weight is: 1
You are correct. Your receipt is 151-117
You are correct. Your receipt is 151-3006 b) If the points A and B are connected to a 38.0 V battery, what is the charge on C3 ?
Problem 5
Problem Weight is: 1 You are correct. Your receipt is 151-7656
A capacitor consisting of two parallel plates of area A = 17.2 m2 and spacing d = 0.15 m is filled with two parallel slabs of dielectric material of equal thickness and with dielectric constants κ1 = 1.60 and κ2 = 7.60, respectively. What is the total capacitance?
Problem 4
???????????????????????????? ???????????????????????????? ???????????????????????????? κ1 ???????????????????????????? ???????????????????????????? ???????????????????????????? ???????????????????????????? ???????????????????????????? ???????????????????????????? κ2 ???????????????????????????? ???????????????????????????? ????????????????????????????
Problem Weight is: 1 You are correct. Your receipt is 151-3827 Problem 6
d/2
d/2
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
5
A capacitor consisting of two parallel plates of plate area A = 15.3 m2 and spacing d = 0.100 m is filled with two equal slabs of dielectric material side by side and with dielectric constants κ1 = 2.60 and κ2 = 7.60, respectively. What is the total capacitance?
????????????????????????????? ????????????????????????????? ?????????????? ??????????????? ?????????????? ??????????????? κ1 κ2 ????????????????????????????? ????????????????????????????? ?????????????????????????????
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
6
A parallel-plate capacitor in air has a plate separation of 1.27cm and a plate area of 27.7cm2. The plates are charged to a potential difference of 230.V and disconnected from the source. The capacitor is then immersed in distilled water. Determine the charge on the plates before immersion. Neglect the conductance of the liquid. You are correct. Your receipt is 151-1357 Determine the charge on the plates after immersion.
d You are correct. Your receipt is 151-1272 Calculate the capacitance after immersion. You are correct. Your receipt is 151-9550 Calculate the voltage after immersion.
Problem Weight is: 1 You are correct. Your receipt is 151-1143
You are correct. Your receipt is 151-5988 Calculate the change in energy of the capacitor.
Problem 7 You are correct. Your receipt is 151-5219 2
A thundercloud has an area A = 310.0 km and is a height d = 1.7 km above the ground. Treat the cloud and the ground as a parallel plate capacitor. Lightning strikes when the voltage between the cloud and the ground reaches V = 96.0 M V (megavolts). The lightning strike completely discharges the ”capacitor” formed by the cloud and the ground.
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.
a) How much charge is transferred by the lightning strike? c Printed from LON-CAPA MSU
You are correct. Your receipt is 151-3313 b) How much energy is dissipated by the lightning strike? You are correct. Your receipt is 151-5336 Problem 8
Licensed under GNU General Public License
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!
Problem 1 A parallel-plate air capacitor of area A = 26.0 cm2 and plate separation d = 2.00 mm is charged by a battery to a voltage 60.0 V. If a dielectric material with κ =5.00 is inserted so that it fills the volume between the plates (with the capacitor still connected to the battery), how much additional charge will flow from the battery onto the positive plate?
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
The Earth is a conducting sphere of radius R = 6370 km. At the Earth’s surface there is an electric field, pointing downward, of magnitude E(R) = 230.0 V/m. a) What is the total charge of the Earth? You are correct. Your receipt is 151-2992 b) Assume that there are no other charges in the Earth’s atmosphere, etc. (Actually there are – but for this problem pretend that there are not.) What is the voltage at the surface of the Earth, if we take the voltage very far from the Earth to be 0 Volts? (Take the dielectric constant of air to be 1.) You are correct. Your receipt is 151-6190 c) Based on these two results, what is the capacitance of the Earth? You are correct. Your receipt is 151-8932 d) Find an expression for the energy density, u(r), in the electric field at a distance r > R, from the centre of the Earth. What is the electric field energy density at r = 13500 km? You are correct. Your receipt is 151-8931 e) Integrate R ∞ your expression for the energy density over all space, R u(r)4πr2 dr. What is the total energy stored in the electric field? You are correct. Your receipt is 151-9218 f) Is your answer above the same as the expression for energy stored in a capacitor, Q2 /(2C)? Choices: Yes, No. You are correct. Your receipt is 151-5536
Problem Weight is: 1 Problem 3 You are correct. Your receipt is 151-8069 Problem 2
2
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
3
a) What is the equivalent capacitance of the four identical capacitors between terminals A and B if C1 = C2 = C3 = C4 = 87.0 µF ? (Give your answer in uF)
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
4
a) Two capacitors (C1 = 6.00 µF, C2 = 19.3 µF) are charged individually to (V1 = 13.7 V, V2 = 5.80 V). The two capacitors are then connected together in parallel with the positive plates together and the negative plates together. Calculate the final potential difference across the plates of the capacitors once they are connected. Problem Weight is: 1 You are correct. Your receipt is 151-1539 b) Calculate the amount of charge that flows from one capacitor to the other when the capacitors are connected together. Problem Weight is: 1 You are correct. Your receipt is 151-5745 c) By how much is the total stored energy reduced when the two capacitors are connected? Problem Weight is: 1
Problem Weight is: 1
You are correct. Your receipt is 151-117
You are correct. Your receipt is 151-3006 b) If the points A and B are connected to a 38.0 V battery, what is the charge on C3 ?
Problem 5
Problem Weight is: 1 You are correct. Your receipt is 151-7656
A capacitor consisting of two parallel plates of area A = 17.2 m2 and spacing d = 0.15 m is filled with two parallel slabs of dielectric material of equal thickness and with dielectric constants κ1 = 1.60 and κ2 = 7.60, respectively. What is the total capacitance?
Problem 4
???????????????????????????? ???????????????????????????? ???????????????????????????? κ1 ???????????????????????????? ???????????????????????????? ???????????????????????????? ???????????????????????????? ???????????????????????????? ???????????????????????????? κ2 ???????????????????????????? ???????????????????????????? ????????????????????????????
Problem Weight is: 1 You are correct. Your receipt is 151-3827 Problem 6
d/2
d/2
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
5
A capacitor consisting of two parallel plates of plate area A = 15.3 m2 and spacing d = 0.100 m is filled with two equal slabs of dielectric material side by side and with dielectric constants κ1 = 2.60 and κ2 = 7.60, respectively. What is the total capacitance?
????????????????????????????? ????????????????????????????? ?????????????? ??????????????? ?????????????? ??????????????? κ1 κ2 ????????????????????????????? ????????????????????????????? ?????????????????????????????
Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter 2014 - PH
6
A parallel-plate capacitor in air has a plate separation of 1.27cm and a plate area of 27.7cm2. The plates are charged to a potential difference of 230.V and disconnected from the source. The capacitor is then immersed in distilled water. Determine the charge on the plates before immersion. Neglect the conductance of the liquid. You are correct. Your receipt is 151-1357 Determine the charge on the plates after immersion.
d You are correct. Your receipt is 151-1272 Calculate the capacitance after immersion. You are correct. Your receipt is 151-9550 Calculate the voltage after immersion.
Problem Weight is: 1 You are correct. Your receipt is 151-1143
You are correct. Your receipt is 151-5988 Calculate the change in energy of the capacitor.
Problem 7 You are correct. Your receipt is 151-5219 2
A thundercloud has an area A = 310.0 km and is a height d = 1.7 km above the ground. Treat the cloud and the ground as a parallel plate capacitor. Lightning strikes when the voltage between the cloud and the ground reaches V = 96.0 M V (megavolts). The lightning strike completely discharges the ”capacitor” formed by the cloud and the ground.
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.
a) How much charge is transferred by the lightning strike? c Printed from LON-CAPA MSU
You are correct. Your receipt is 151-3313 b) How much energy is dissipated by the lightning strike? You are correct. Your receipt is 151-5336 Problem 8
Licensed under GNU General Public License
