Exam 2
Closed book exam. A calculator is allowed, as is one 8.511” sheet of paper with your own written notes. Please show all work leading to your answer to receive full credit. Numerical answers should be calculated to 2 significant digits. Exam is worth 100 points, 25% of your total grade.
UF Honor Code: “On my honor, I have neither given nor received unauthorized aid in doing this exam.”
1. An RC circuit is discharged by closing a switch at time t = 0. The initial potential difference across the capacitor is 5 V. The potential difference across the capacitor drops to half of its value in 35 ms.
(a)[6 points] What is the time constant of the circuit?
(b)[4 points] If the total resistance in the circuit is 10 k, what is the capacitance?
2. [8 points] In the circuit shown, the resistances are, , and . The battery voltages are and . What is the current (in amps) flowing through the battery with potential difference?
3. [6 points] Two identical amounts (volumes) of copper are formed into two cylindrical rods, the first of length Land the second of length L/2. If the resistances of the two volumes (measured between the two ends) are and respectively, what is ?
4. [6 points] A large flat non-conducting sheet has an electric charge density of , where , as measured in the rest frame of the sheet. What is the charge density “seen” by an electron traveling at a velocity of parallel to the surface of the sheet?
5. [6 points] Galaxy A is reported to be receding from us at a speed of 0.41c. Galaxy B, located in precisely the opposite direction, is found to be receding from us at the same speed. What recessional speed would an observer on Galaxy A find for Galaxy B?
6. [6 points] An electron is accelerated from rest by a potential difference of 10,000 V. It then enters a uniform magnetic field of magnitude 0.05 T with its velocity perpendicular to the direction of the field. Calculate the radius in meters of its path in the magnetic field. The mass of the electron is .
7. The rectangular-shaped loop shown in the figure is carrying a current i = 2A in the clockwise direction shown. The length of the vertical sides is 7cm and the length of the horizontal sides is 3.5 cm. A uniform magnitude field B= 0.05T makes an angle =30 with respect to the plane of the loop.
(a) [6 points] What is the magnitude of the torque acting on the loop
if the left side is connected to a hinge?
(b) [6 points] If the loop is free to rotate about its hinge due to the torque, by how much will the potential energy of the loop change when the torque becomes zero?
8. [8 points] A long straight wire carries a current in the horizontal direction shown. Below it is a square loop of side length carrying a current in the clockwise direction shown. The distance between the top of loop to the long straight wire is distance a, which you can take to be much smaller than b ().If the mass of the loop is 10 g, what is the maximum distance a such that the loop is attracted to the wire with current with a force that overcomes the force of gravity? (the acceleration due to gravity points in the direction).
9. [6 points] A horizontal power line carries a current of 3000A from south to north. Earth's magnetic field, with a magnitude of 60T, is directed toward the north with a dip angle 60° downward into the Earth relative to the horizontal. Find the magnitude and direction (use compass directions) of the magnetic force acting on a 100 m length of power line.
10. [8 points] An infinitely long insulated wire carrying a current I = 100 A is bent into the shape shown (straight line plus circle of radius R=3 cm with the currents in the direction shown). Find the magnitude of the field B at the center of the circle.
11. [6 points] A conductor has a cylindrical cross section with a radius a = 2 mm. Inside, a cylindrical cut-out hole (non-conducting) is made as shown, where the radius of the cut-out is b = 0.5 mm and the distance between the center of the main conductor and the center of the cut-out is d = 1 mm. The magnitude of the current density in the conductor is. What is the magnitude of the magnetic field at a radius of mm from the center of the conductor along a line connecting to the center of the cut-out? [Hint: try using the superposition principle.]
12. A rectangular loop of wire of sides is moving with constant speed v into a region of uniform magnetic field of magnitude B directed out of the paper as shown in the figure (the long side is along the direction of motion).
(a)[6 points] What is the magnitude of the induced EMF in the
wire and the direction of the induced current just
after the loop enters the region of magnetic field?
(b)[6 points] If the total resistance of the wire is R, what is the power dissipated by the loop?
13. [6 points] A circular loop of wire of radius 30 cm sits in the x-y plane in a region where there is a uniform magnetic field of , where B0= 0.5 T. The magnetic field is now increased at a constant rate such that it reaches three times its original strength in 20 s. What is the magnitude of the induced EMF in the wire loop during this time?
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