Good Luck! Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter PH. Electromagnetism and Optics - Winter PH

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1 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 = 100. is wrong, but = 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 capa142@physics.mcgill.ca, i ll be glad to help you. Good Luck! Review Problem 1 2 a) Two insulated balls of mass g hang from the same support point by massless insulating threads of length l (as shown in the diagram.) A total positive charge of q = C is added to the system. Half this charge is taken up by each ball, distributed uniformly, and the balls spread apart to a new equilibrium position. Assuming that the balls hang essentially vertically before the charge is added, what is the tension in each thread before the charge is added? You are correct. Your receipt is b) If θ=23.0, what is the length, l, of each string? You are correct. Your receipt is Due Date: Due never Problem 2 Find the magnitude of the electric field a distance z=9.00 cm above the center of a square loop (side a=2.60 cm) carrying uniform line charge λ= C/m. You are correct. Your receipt is Problem 3

2 3 For the configuration shown in the figure below, suppose that a = 5.12 cm, b = 21.0 cm, and c = 26.0 cm. 4 A solid conducting sphere of radius 2.17 cm has a charge 7.72 µc. A conducting spherical shell of inner radius 3.84 cm and outer radius 5.08 cm is concentric with the solid sphere and has a charge µc. a) Calculate the electric field at r = 1.32 cm from the center of this charge configuration. You are correct. Your receipt is b) Calculate the electric field at r = 3.41 cm from the center of this charge configuration. You are correct. Your receipt is c) Calculate the electric field at r = 4.51 cm from the center of this charge configuration. Furthermore suppose that the electric field at a point 9.5 cm from the center is 3.64E+3 N/C radially inward, while the electric field at a point 46.8 cm from the center is 2.15E+2 N/C radially outward. a) Calculate the charge on the insulating sphere. You are correct. Your receipt is You are correct. Your receipt is d) Calculate the electric field at r = 6.00 cm from the center of this charge configuration. You are correct. Your receipt is Problem 5 b) Calculate the net charge on the hollow conducting sphere. You are correct. Your receipt is c) Calculate the total charge on the inner surface of the hollow conducting sphere. You are correct. Your receipt is d) Calculate the total charge on the outer surface of the hollow conducting sphere. An infinite sheet of charge that has a surface charge density of 23.9 nc/m2 lies in the yz plane, passes through the origin, and is at a potential of 1.48 kv at the point y = 0, z = 0. A long wire having a linear charge density of 80.4 nc/m lies parallel to the y axis and intersects the x axis at x = 2.69 m. a) Determine the potential along the x axis at x = m between wire and sheet. You are correct. Your receipt is You are correct. Your receipt is b) What is the potential energy of a 2.09 nc charge placed at x = m? Problem 4 You are correct. Your receipt is Problem 6

3 5 Consider two thin, conducting, spherical shells as shown in cross-section in the figure below. 6 Problem 7 A 1.83 nf parallel-plate capacitor is charged to an initial potential difference Vi = 120 V and then isolated. The dielectric material between the plates is mica (κ = 5.46). a) How much work is required to withdraw the mica sheet? You are correct. Your receipt is b) What is the potential difference of the capacitor after the mica is withdrawn? You are correct. Your receipt is Problem 8 The inner shell has a radius r1 = 18.9 cm and a charge of 10.0 nc. The outer shell has a radius r2 = 27.3 cm and a charge of nc. Calculate the equivalent capacitance between the points a and b in the figure below, if C1 = 3.66 µf, C2 = 2.35 µf, C3 = 7.82 µf, C4 = 3.66 µf and C5 = 2.35 µf. a) Calculate the electric field E at r = 12.3 cm. You are correct. Your receipt is b) Calculate the electric field E at r = 21.1 cm. You are correct. Your receipt is c) Calculate the electric field E at r = 42.7 cm. You are correct. Your receipt is d) Calculate the electric potential V at r = 12.3 cm, with V = 0 at r =. You are correct. Your receipt is e) Calculate the electric potential V at r = 21.1 cm. You are correct. Your receipt is f) Calculate the electric potential V at r = 42.7 cm. You are correct. Your receipt is You are correct. Your receipt is Due never Problem 9

4 7 A proton moving in the plane of the page has a kinetic energy of 5.90 MeV. It enters a magnetic field of magnitude B = 1.13 T directed into the page, moving at an angle of θ = 45.0 with the straight linear boundary of the field, as shown in the figure below. 8 An electric utility company supplies a customer s house from the main power lines (115 V) with two copper wires, each of which is 54.3 m long and has a resistance of Ω per 306 m. a) Calculate the voltage at the customer s house for a load current of 110 A. You are correct. Your receipt is b) For this load current, calculate the power that the customer is receiving. You are correct. Your receipt is c) Calculate the power lost in the copper wires. You are correct. Your receipt is Problem 11 a) Calculate the distance x from the point of entry to where the proton leaves the field. A singly charged ion (charge q = +1.60e-19 C) completes five revolutions in a uniform magnetic field of magnitude 4.98E2 T in 1.65 ms. Calculate the mass of the ion in kilograms. You are correct. Your receipt is Due never You are correct. Your receipt is b) Determine the angle θ between the boundary and the proton s velocity vector as it leaves the field. You are correct. Your receipt is Problem 10 Problem 12

5 9 Two circular loops are parallel, coaxial, and almost in contact, 1.16 mm apart (see figure below). 10 A conducting rod of length l = 34.8 cm is free to slide on two parallel conducting bars, as shown in the figure below. Two resistors R1 = 2.01 Ω and R2 = 4.94 Ω are connected across the ends of the bars to form a loop. A constant magnetic field B = 2.75 T is directed perpendicular into the page. An external agent pulls the rod to the left with a constant speed of v = 7.83 m/s. Each loop is 13.3 cm in radius. The top loop carries a clockwise current of I = 135 A. The bottom loop carries a counterclockwise current of I = 135 A. a) Calculate the magnitude of the current in R1. a) Calculate the magnetic force that the bottom loop exerts on the top loop. You are correct. Your receipt is You are correct. Your receipt is b) Calculate the magnitude of the current in R2. b) The upper loop has a mass of kg. Calculate its acceleration, assuming that the only forces acting on it are the force in part (a) and its weight. You are correct. Your receipt is You are correct. Your receipt is c) Calculate the total power delivered to the resistance of the circuit. Problem 13 You are correct. Your receipt is d) Calculate the magnitude of the applied force that is needed to move the rod with this constant velocity. You are correct. Your receipt is Problem 14

6 11 12 The figures below show two different situations where a current may be induced in a loop by Faraday s Law, with the direction determined by Lenz Law. The magnetic field is shown by the x s in Fig. 2. Select ALL correct answers (i.e. B, AC, BCD) for the current in the loop. (The compass directions are defined in the usual way.) Figure 1: Figure 2: Three capacitors of capacitance C1 = 2.00 µf, C2 = 5.50 µf, and C3 = 16.0 µf are connected to a 40.0 V battery as shown. a) Calculate the charge on C3. You are correct. Your receipt is b) Calculate the voltage across C1. Choices: True, False. A. fig2: Loop moving East, induced current a. B. fig1: Magnet moving East, induced current a. C. fig2: Loop moving South, no induced current. D. fig2: Loop moving North, induced current b. Due never You are correct. Your receipt is Problem 15 You are correct. Your receipt is Problem 16

7 13 a) What is the equivalent capacitance of the four identical capacitors between terminals A and B if C1 = C2 = C3 = C4 = 53.0 µf? (Give your answer in uf) 14 The switch in the figure below is thrown closed at t = 0. E = 18 V and R = 1.13 Ω. Before the switch is closed, the capacitor is uncharged, and all currents are zero. You are correct. Your receipt is b) If the points A and B are connected to a 69.0 V battery, what is the charge on C3? You are correct. Your receipt is Due never a) Determine the current in L, C and R the instant after the switch is closed. (Enter the values in this order). You are correct. Your receipt is b) Determine the potential difference across L, C and R the instant after the switch is closed. (Enter the values in this order). Problem 17 You are correct. Your receipt is A doubly ionized atom (charge = +2e) whose mass is 1.16E26 kg is accelerated by a voltage of 2050 V and enters a region where a uniform magnetic field B = T acts perpendicular to its motion. a) What is the radius of curvature of the path of the ion in the B-field? c) Determine the current in L, C and R long after the switch is closed. (Enter the values in this order). You are correct. Your receipt is You are correct. Your receipt is b) What is its period of revolution? d) Determine the potential difference across L, C and R long after the switch is closed. (Enter the values in this order). You are correct. Your receipt is You are correct. Your receipt is Problem 19 Problem 18

8 15 The use of superconductors has been proposed for the manufacture of power transmission lines. A single coaxial cable (see figure below) could carry 1.46E+3 MW (the output of a large power plant) at 215 kv dc, over a distance of 1500 km without loss. 16 A voltage v = (100 V) sin ωt (in SI units) is applied across a series combination of a 1.82 H inductor, a 14.8 µf capacitor, and a 10.5 Ω resistor. a) Determine the angular frequency, ω0 at which the power delivered to the resistor is a maximum. You are correct. Your receipt is b) Calculate the power at that frequency. You are correct. Your receipt is c) Determine the two angular frequencies ω1 and ω2 at which the power delivered is one-half the maximum value. [The Q of the circuit is approximately ω0 /(ω2 - ω1 ).] Enter the smaller one first. You are correct. Your receipt is Due never An inner wire with a radius of a = 2.15 cm, made from the superconductor Nb3 Sn, carries the current in one direction. A surrounding superconducting cylinder, of radius b = 4.93 cm, would carry the return current. a) In such a system, what is the magnetic field at the surface of the inner conductor. Problem 21 A power supply with Vrms = 115 V is connected between points a and d in the figure below. You are correct. Your receipt is b) What is the magnetic field at the inner surface of the outer conductor? You are correct. Your receipt is As shown, R = 38.2 Ω, L = 142 mh and C = 76.1 µf. At what frequency will it deliver a power of 250 W? Enter one of the two possible frequencies (in Hz). c) How much energy would be stored in the space between the conductors in a 1500 km superconducting line? You are correct. Your receipt is Due never You are correct. Your receipt is d) What is the pressure exerted on the outer conductor? You are correct. Your receipt is Problem 20 Problem 22

9 17 A plane electromagnetic wave of intensity 5.91 W/m2 strikes a small pocket mirror, of area 38.7 cm2, held perpendicular to the approaching wave. a) What momentum does the wave transfer to the mirror each second? 18 Jupiter, seen from the Earth, has an angular diameter of AD = 45.6 arc seconds. There are 3600 arc seconds in a degree. How large would the aperture (lens or mirror) on a telescope need to be, in order to have N = 20 times finer resolution than this (so it could make a clear image of Jupiter)? Assume the telescope is viewing Jupiter in λ = 500 nm light. You are correct. Your receipt is You are correct. Your receipt is Due never b) Calculate the force that the wave exerts on the mirror. You are correct. Your receipt is Due never 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. Problem 23 Lasers have been used to suspend spherical glass beads in the Earth s gravitational field. If a bead has a mass of 1.27 µg and a density of g/cm3: a) Determine the radiation intensity needed to support the bead. You are correct. Your receipt is b) If the beam has a radius of cm, what power is required for this laser? You are correct. Your receipt is Due never Problem 24 Light from a gas discharge tube falls at normal incidence on a diffraction grating. Because of overlap of various orders, two lines superpose at theta=25.0 degrees. If the wavelengths of the lines are nm and nm, find the grating spacing (in µm). You are correct. Your receipt is Problem 25 Printed from LON-CAPA c MSU Licensed under GNU General Public License

Good Luck! Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter PH. Electromagnetism and Optics - Winter PH

Good Luck! Mlanie LaRoche-Boisvert - Electromagnetism Electromagnetism and Optics - Winter PH. Electromagnetism and Optics - Winter 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,