Print Name _______________________

 

ID Number _______________________

 

Your lecture section time ____________

 

 

Physics 241E, Test No. 1

September 30, 1996

 

 

First do the problems you find easiest, then do the harder ones. It is best to do them first on scratch paper and then to copy the solutions on the test paper. Show your complete solutions, including diagrams, reasoning, and algebra. Scratch out anything you do not want the grader to consider. Undeleted, incorrect jottings will lower your grade. So will answers without an indication of where you got them from. Your grade for each problem will be based on the grader's impression of your understanding of the problem, as well as on the correct answer. You may use one half of a 8.5" x 11" sheet of paper on which you have written what you please. No other notes or books are allowed during the exam.

 

 

Numerical answers must include units, and must be written with the correct number of significant figures.

 

Write out the authorized form of the pledge here, and sign it.

 

______________________________________________________________________________

 

______________________________________________________________________________

 

______________________________________________________________________________

 

______________________________________________________________________________

 

 

Signed _______________________

 

  1. On the planet of Tatouine the distribution of molecular speeds in a gas is NOT the Maxwell-Boltzmann distribution

    2.  

    but rather is

     

    f(v) dv = Cv2 dv ; v0 v 0

    = 0 ; v v0

     

    as shown in the figure.

     

    a) (7 points) What is C in terms of v0 if f(v) is normalized to 1 as is the Maxwell Boltzmann distribution?

     

     

     

     

     

     

    b) (7 points) What is the average or mean speed of the molecules?

     

     

     

     

     

     

     
      1. (7 points) What is the root mean square speed of the molecules?

       

       

       

       

       

       

       
        1. (4 points) If the gas is helium, what is the average kinetic energy of the molecules? (Let the molecular mass be m).

         

         

         

         

         

         

         

         

        1. One mole of an ideal gas at T = 300 K expands reversibly and isothermally between V1 = 30 L and V2 = 60 L. (R = 8.314 J/mol.K)

          2.  

            1. (10 points) Find the entropy change in the gas.

             

             

             

             

             

             

             

             

             
              1. (5 points) What is the total (gas + surroundings) entropy change?

             

             

             

            c)  (10 points) If the gas is then compressed at the same temperature until it reaches V3 = 50 L, what has been its change in entropy from point 1, to point 3?

             

             

             

             

             

            1. An engine uses a monoatomic gas to perform a three step cycle:

             

            From 1 ® 2 it performs an adiabatic expansion (P1 = 4 atm,

            V1 = 10 L; P2 = 1.75 atm, V2 = 15 L). From 2 ® 3 it under-

            Goes an isobaric compression and from 3 ® 1 it undergoes

             

            an isochoric transformation. Indicate the direction of heat

            flow in the diagram.

             
              1. (15 points) Calculate the heat flow between points 1 and

                2. 2, Q12, between 2 and 3, Q23, and between 3 and 1, Q31.

                 

                 

                 

                 

                 

              2. (5 points) Calculate the net work performed by the engine.

                3.  

                 

                 

                 

                 

                 

                 

                 

                 

                 

                 

                 

              3. (5 points) Calculate the efficiency of the engine.

             

             

             

             

             

             

            1. A 3 m C charge is uniformly distributed on a ring of radius 8 cm with its center at z = 0 and central axis along the z axis. A point charge of -2 m C is placed at z = -4 cm, as shown in the figure. (1/4m e 0 = 8.99 x 109 N.m2/C2, m means 10-6)

             

              1. (10 points) What is the force acting on a 1 m C point charge at

                2. the origin by the -2 m C point charge? What is the force acting

                on the m C charge by the ring? Force must be given in vector

                form.

                 

                 

              2. (13 points) The 1 m C charge is now moved to z = 4 cm. What is the force acting on it

                3. due to the ring alone? What is the total force acting on it due to the ring and -2 m C point charge?

                 

                 

                 

                 

                 

                 

                 

                 

                 

                 

              3. (2 points) Is there a point on the z-axis at (i) z > 0, (ii) z < 0 where the 1 m C charge feels no force due to the ring and -2 m C charge? Give yes or no answer to both (i) and (ii).

             

            Print Name _______________________

             

            ID Number _______________________

             

            Your lecture section time ____________

             

             

            Physics 241E, Test No. 2

            October 28, 1996

             

             

            First do the problems you find easiest, then do the harder ones. It is best to do them first on scratch paper and then to copy the solutions on the test paper. Show your complete solutions, including diagrams, reasoning, and algebra. Scratch out anything you do not want the grader to consider. Undeleted, incorrect jottings will lower your grade. So will answers without an indication of where you got them from. Your grade for each problem will be based on the grader's impression of your understanding of the problem, as well as on the correct answer. You may use one half of a 8.5" x 11" sheet of paper on which you have written what you please. No other notes or books are allowed during the exam.

             

             

            Numerical answers must include units, and must be written with the correct number of significant figures.

             

            Write out the authorized form of the pledge here, and sign it.

             

            ______________________________________________________________________________

             

            ______________________________________________________________________________

             

            ______________________________________________________________________________

             

            ______________________________________________________________________________

             

             

            Signed _______________________

             

              

             

            Possibly useful quantities:

             

            e 0 = 8.85 x 10-12C2/N·m2, e = 1.60 x 10-19 C, NA = 6.02 x 1023/mol, me = 9.11 x 10-31 kg

             

             

             

            1. An infinitely long conducting cylinder of radius A = 1 cm with a linear charge density of l 1 = 3 nC/m is centered on the axis. It is surrounded by a conducting cylinder having an inner radius B = 3 and outer radius C = 4 cm carrying a net charge density of l 2 = -2 nC/m. What is the electric field (magnitude and direction) at

              1. [5 points] r = 0.5 cm?

                2.  

                 

                 

                 

                 

                 

                 

                 

              2. [5 points] r = 2.0 cm?

                3.  

                 

                 

                 

                 

                 

                 

                 

              3. [5 points] What is the surface charge density on the inner surface of the outer

                4. conductor?

                 

                 

                 

                 

                 

                 

                 

              4. [5 points] r = 3.5 cm?

                5.  

                 

                 

                 

                 

                 

                 

              5. [5 points] r = 5.5 cm?

             

             

             

             

            1. A 0.2 m long Nichrome wire of unknown resistance is connected between the terminals of a 3.00 V battery. Energy is dissipated in the wire at a rate of 0.54 W.

             

              1. [7 points] What is the resistance of the Nichrome wire?

                2.  

                 

                 

                 

                 

                 

                 

                 

                 

                 

                 

              2. [6 points] The Nichrome wire is now disconnected from the battery and connected to a current source of 0.2 A. What is the power dissipation?

                3.  

                 

                 

                 

                 

                 

                 

                 

                 

                 

              3. [7 points] What is the electric field within the wire in b)?

                4.  

                 

                 

                 

                 

                 

                 

                 

              4. [5 points] Three identical 0.2 m long wires are twisted together to form a single 0.2 m long wire which is then connected to the 3.00 V battery from a). Calculate the power dissipation.

             

             

             

             

             

             

             

            1. A parallel plate 10 nF capacitor is connected to a battery which keeps a potential difference of 30 V between the plates. If the distance, d, between the plates is doubled:

             

              1. [6 points] What is the new capacitance?

                2.  

                 

                 

                 

                 

                 

                 

                 

                 

              2. [6 points] What is the change in potential energy stored in the capacitor?

                3.  

                 

                 

                 

                 

                 

                 

                 

                 

                 

                 

              3. [6 points] What is the change in the charge stored on the capacitor?

                4.  

                 

                 

                 

                 

                 

                 

                 

                 

              4. [7 points] If the battery is disconnected, how much work needs to be done to increase the distance between the plates from 2d to 3d? (Hint: it is the charge, Q, that is kept constant now.)

             

             

             

             

             

             

             

            1. A circular (R = 8 cm) ring of charge Q = 10 m C lies in the plane, centered on the origin. A point charge of -10 m C lies on the axis at z = .6 cm as shown.

              1. [8 points] What is the electric potential at the origin due only to the ring ?

                2.  

                 

                 

                 

                 

                 

                 

              2. [8 points] What is the total electric potential at the origin due to the ring and the point charge ?

                3.  

                 

                 

                 

                 

                 

                 

                 

                 

              3. [9 points] Where on the axis (in addition to z = ± ¥ ) is the potential zero?

             

             

            Print Name _______________________

             

            ID Number _______________________

             

            Your lecture section time ____________

             

             

            Physics 241E, Test No. 3

            November 26, 1996

             

             

            First do the problems you find easiest, then do the harder ones. It is best to do them first on scratch paper and then to copy the solutions on the test paper. Show your complete solutions, including diagrams, reasoning, and algebra. Scratch out anything you do not want the grader to consider. Undeleted, incorrect jottings will lower your grade. So will answers without an indication of where you got them from. Your grade for each problem will be based on the grader's impression of your understanding of the problem, as well as on the correct answer. You may use one half of a 8.5" x 11" sheet of paper on which you have written what you please. No other notes or books are allowed during the exam.

             

             

            Numerical answers must include units, and must be written with the correct number of significant figures.

             

            Write out the authorized form of the pledge here, and sign it.

             

            ______________________________________________________________________________

             

            ______________________________________________________________________________

             

            ______________________________________________________________________________

             

            ______________________________________________________________________________

             

             

            Signed _______________________

             

             

             

             

             Possibly useful quantities:

             

            e 0 = 8.85 x 10-12C2/N·m2, e = 1.60 x 10-19 C, m 0 = 4p x 10-7 T× m/A, me = 9.11 x 10-31 kg

             

             

            1. Singly charged ions (i.e., with charge q = 1.6 ´ 10-19C) are injected into a uniform transverse magnetic field of 0.11T. When the initial energy of the ions is 0.1 MeV, they describe a circular path of radius r = 0.82m.

             

              1. [3 points] Express the kinetic energy of the ions in Joules.

                2.  

                 

                 

                 

                 

                 

                 

                 

                 

                 

              2. [8 points] By observing that the magnetic field exerts a centripetal force on the ions, find an expression for their mass, m, in terms of: the magnetic field B, their velocity v, their charge q, and the radius r.

                3.  

                 

                 

                 

                 

                 

                 

                 

                 

              3. [10 points] Find the value of m in kg.

             

             

             

             

             

             

             

             

             

             

             

            d) [4 points] What electric field, , should be applied in order to make the ions pass undeflected by the magnet field ? [Hint: the force exerted by should balance the force exerted by .]

             

             

             

             

             
            1. A long straight wire and a rectangular wire loop arranged as shown carry currents

            I1 = 10A and I2 = 5A respectively.

              1. [6 points] Calculate the magnetic field due to the long wire at distances r = 10 cm and r = 20 cm from it.

                2.  

              2. [6 points] Indicate on the figure the direction of the forces acting on the four sides of the loop due to the long wire.

                3.  

                 

                 

                 

              3. [8 points] Calculate the forces acting on the two long sides of the loop due to the long wire.

                4.  

                 

                 

                 

                 

                 

                 

                 

                 

                 

                 

                 

              4. [5 points] Find the total force acting on the loop.

             

             

             

             

             

             

            1. A wire ring of radius 1 cm is located near the center of a long solenoid. The solenoid, of radius 2 cm and length 40 cm, has 200 turns of wire. The area of the ring is inclined at 60° to the axis of the solenoid, as shown in the figure.

              1. [5 points] What is the magnetic field inside the solenoid if I = 1A?

             

             

             

             

             

             

             

            b) [5 points] What is the magnetic flux through the wire ring?

             

             

             

             

             

             

             

             

            c) [6 points] If the current I = 1A is switched off in 1 ms, find the magnitude and direction of the induced EMF in the ring.

             

             

             

             

             

             

             
              1. [7 points] The ring has a resistance of R = 2W . If a time-dependent current

            I = sin(377t)A is applied to the solenoid, find an expression for the power dissipation in the ring.

             

             

             

             

             

            e) [2 points] What is the average power dissipation?

             

             

             

             

             

             

            1. Consider the circuit shown wherein and each resistor has a resistance R = 4W .

             

              1. [10 points] Simplify the circuit by replacing combinations of resistors in series or parallel by equivalent resistances. Calculate the equivalent resistances and draw the simplified circuit, indicating the values of the resistances.

                2.  

                 

                 

              2. [15 points] What current flows through each battery (assume no internal resistance)? Indicate the direction of flow on the circuit diagram.

             

            Final Exam - Physics 241E

             Date: 16 December 1996

             

             

            There are 24 questions on this exam. Read them all before you begin and then start with the easiest. You are NOT penalized for guessing so attempt them all. Mark your answers on the answer sheet with a Number 2 pencil. Write out and sign the pledge on the back of the answer sheet. Be sure to mark in your Social Security Number.

             

            Using different numbers of significant digits can result in numerical answers slightly different from those given. In each case, choose the BEST answer from those listed.

             

            You may bring in one 81/2 x 11 sheet of paper containing any hand written material you wish. No copied material allowed.

             

            Before you leave, you will be asked to hand in your question sheet with your name written on it. It is an Honor Violation to discuss the exam in any way with anyone who has not yet taken it. Note that the exam is given on Tuesday (Dec. 10) morning, Wednesday (Dec. 11) afternoon, and Monday (Dec. 16) morning. It is also an Honor Violation to attempt the exam more than once.

             

             

             

            Possibly Useful Quantities

             

            R = 8.31 J/mol·K

            G = 6.67 ´ 10-11m3/kg× s2

             

             

             

             

            If you plan to take Physics 242E next semester hold onto your text; you will need it.

             

              1. How much energy is stored in a solenoid of length l = 0.5 m, radius r = 0.05 m, total number of turns N = 500 and carrying a current I = 1.5 A?

             

            a. 7.85 ´ 10-3 J

            b. 1.26 ´ 10-3 J
              1. 5.55 ´ 10-3 J
              2. 9.86 ´ 10-5 J
              3. 6.16 ´ 10-4 J

             

            1. A rectangular wire loop of area A = 40 cm2 lies in the plane with one edge along the axis. It carries a current on 6.0 A. A uniform magnetic field of 0.84 T is directed the direction. What torque with respect to the axis does the loop feel?

              1. 7.14 ´ 10-3N × m
              2. 10.1 ´ 10-3N × m
              3. 5.04 ´ 10-3N × m
              4. 20.2 ´ 10-3N × m

            e. 0

             

            3) A series RLC circuit, driven with e rms = 120 V at a frequency of 60 Hz, contains a resistance R = 50 W , an inductance with XL = 80 W , and a variable capacitance C. What are C and the average power dissipation when the latter is maximized?
              1. 33m F, 144 W
              2. 22 m F, 108 W
              3. 33 m F, 72 W
              4. 33 m F, 288 W
              5. 44m F, 312 W

             

             4) A conducting slab of thickness b is placed somewhere between the plates of a parallel place capacitor, at a distance x from one of the plates, as shown in the figure. Find the capacitance if b = 0.25a.

              1. 1.33
              2. 1.38
              3. 1.25
              4. 1.43
              5. 1.17

             

             

            1. A 4 cm thick slab with a uniform charge density of 1 m C/m3 lies in the plane as shown. A spherical hole of radius 2 cm and centered on the origin is cut out of the slab. What is the electric field at the point = 3.5 cm ?
              1. 2.02 kV/m
              2. 1.93 kV/m
              3. 2.26 kV/m
              4. 0.75 kV/m
              5. 1.78 kV/m

             

             

             

             

             

             

            1. Two charges, q1 = 5 nC, and q2 = -1 nC, are positioned at O º (0,0) and Q º (4 cm, 0) as shown in the figure. How much work has to be done to bring a 1 nC charge from infinity to the point P º (0,3 cm)?
              1. 1.39 ´ 10-6J
              2. 1.32 ´ 10-6J
              3. 4.64 ´ 10-5J
              4. 4.79 ´ 10-5J
              5. 1.68 ´ 10-6J

             

             

            1. One mole of an unknown monatomic gas is contained at a pressure of 1.2 atmospheres in a 25 liter container. Gas atoms leaking from the container are observed to have an rms speed of 529 m/s. What is the mass of the gas atoms?
              1. 6.68 ´ 10-27 kg
              2. 5.34 ´ 10-26 kg
              3. 4.68 ´ 10-26 kg
              4. 3.34 ´ 10-27 kg
              5. 1.67 ´ 10-26 kg

             

              

            1. A 100 pF capacitor is charged to 100 V. After charging, the battery is disconnected and the capacitor is connected in parallel to another capacitor. If the final voltage across the capacitor is 60 V, what is the capacitance of the second capacitor?
              1. 30 pF
              2. 333 pF
              3. 233 pF
              4. 66.7 pF
              5. 100 pF

             

             

              

            1. The AC circuit in the figure has a capacitor with capacitance C = 1.5 m F and a negligible resistance. The rms voltage of 40 V. What is the rms current if the frequency is 100 Hz?
              1. 3.77 ´ 10-2 A

            b) 1.88 ´ 10-2 A

            c) 2.37 A

            d) 4.16 ´ 10-2 A

            e) 2.83 ´ 10-2 A

             

             
            1. Two equal positive charges, q2 = 0.3 m C, and one positive charge q1 = 0.2 m C are placed at the corners of an equilateral triangle of side l = 1 m as in the figure. What is the electric field in the middle of the triangle?
              1. 900 N/C down
              2. 2.70 ´ 103 N/C up
              3. 0
              4. 2.70 ´ 103 N/C down
              5. 900 N/C up

             

             

             

            11. The power consumption of a refrigerator is rated at 740 W. What is the maximum amount of heat it can remove in 1 minute if the inside temperature of the refrigerator is

            0° C and it exhausts into a room at 20° C?

              1. 160 kJ
              2. 30 kJ
              3. 606 kJ
              4. 303 kJ
              5. 452 kJ

             

             

             

              

            1. The electric field at which dielectric breakdown occurs in air is 3 x 106 N/C. An isolated spherical conductor has a radius of 1.5 m. Calculate the maximum electric potential of the sphere (with respect to zero at infinity) before dielectric breakdown occurs.
              1. 3 ´ 106V

            b) 6 ´ 106V

            c) 5 ´ 106V

            d) 9 ´ 106V

            e) 4.5 ´ 106V

             

             

             

             

             

             

             
            1. Consider the circuit shown with C1 = 2.5 m F, C2 = 1.5 m F, and R = 30 kW . The battery charges the capacitors to 12 V and is then disconnected. At time t = 0 the switch S1 is closed. What will the current through R be at t = 0.1 s?
              1. 11 m A
              2. 105 m A
              3. 43 m A
              4. 76 m A
              5. 174 m A

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

            1. A parallel plate capacitor is constructed from square metal plates 10 cm ´ 10 cm separated by 0.5 mm and a 24 volt battery is attached. A 0.5 mm thick slab of dielectric (k = 5) is inserted a distance x as shown. What force is felt by the dielectric?
              1. 2.04 ´ 106 N
              2. 1.27 ´ 106 N
              3. 2.55 ´ 106 N
              4. 5.09 ´ 106 N
              5. 1.59 ´ 106 N

             

             

             

             

             

             

             

            1. At the equator, a 1000-turn coil with a cross-sectional area of 300 cm2 and a resistance of 7.5 W is aligned with its plane perpendicular to the earth's magnetic field of 7 ´ 10-4 T. If the coil is flipped over, how much charge flows through it?
              1. 6.0 ´ 10-4C
              2. 1.4 ´ 10-4C
              3. 2.1 ´ 10-3C
              4. 5.6 ´ 10-3C
              5. 2.8 ´ 10-3C

             

             

             

             

             

             

            1. A circular loop of wire 70 mm in radius carries a current of 100 A. Find the magnetic field strength at the center of the loop.
              1. 3.1 mT
              2. 1.3 mT
              3. 4.1 mT
              4. 0.9 mT
              5. 2.2 mT

             

             

             

             

             

            1. An electron is fired directly toward the center of a large metal plate that has a surface charge density of -2.0 ´ 10-6C/m2. If the initial kinetic energy of the electron is 150 eV and if the electron stops just as it reaches the plate, how far from the plate was it fired?
              1. 0.11 mm
              2. 0.22 mm
              3. 0.88 mm
              4. 0.66 mm
              5. 0.44 mm

             

             

             

             

             

             

             

             

             

             

            1. A transformer has 500 primary turns and 30 secondary turns. A voltage of Vrms = 120 V is applied across the primary coil. If the secondary coil is now connected to a resistive load of 15 W , what is the current (Irms) in the primary coil?
              1. 29 mA
              2. 13 mA
              3. 6.4 mA
              4. 3.2 mA
              5. 10 mA

             

             

             

             

             

            1. In the circuit diagram,

            . Find the amplitude of the voltage measured across the inductor. [Hint: phase of voltage VL(t) across the inductor leads phase of current by 90° ]

             

             

             

            1. An ideal gas with g = 1.4 has initial pressure p1 = 1 atm, volume V1 = 5 L and temperature T1 = 20° C. It expands adiabatically and quasi-staticly to twice its original volume. What is its final temperature?
              1. 30 K
              2. 230 K
              3. 222 K
              4. 288 K
              5. 152 K

             

             

             

             

             

            1. A metal rod is forced to move at a constant speed of 50 cm/s along two parallel frictionless metal rails, connected by a strip of metal at one end (see figure). A uniform magnetic field

            points out of the page. If the rod has a resistance of 10 W and the rails and strip have negligible resistance, at what rate is energy being transformed into thermal energy?

              1. 0.16 mW
              2. 0.04 mW
              3. 0.02 mW
              4. 0.01 mW
              5. 0.08 mW

             

             

             

             

             

            1. Two infinitely long wires with a charge density and two with a charge density of form a grid in the

            plane as shown. What is the electric field at the origin?

             

             

             

             

             

             

            1. A spherical non-conducting shell with density

            has an inner radius r = 12 cm and an outer radius R = 20 cm. What is the magnitude of the electric field, E, at r = 0.15 m?

              1. 5.44 N/C
              2. 1.36 ´ 10-2 N/C
              3. 0.69 N/C
              4. 2.76 N/C
              5. 3.98 N/C

             

             

             

             

             

            1. A heat engine works between two reservoirs at Th = 450 K and Tc = 325 K. During each cycle the engine absorbs Qh = 1200 J of work. What is the ratio of the work done by the engine to that of a Carnot cycle operating under the same conditions?
              1. 0.43
              2. 0.5
              3. 0.39
              4. 0.33
              5. 0.6