# 2R R R 2R. Phys Test 1

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1 Group test. You want to calculate the electric field at position (x o, 0, z o ) due to a charged ring. The ring is centered at the origin, and lies on the xy plane. ts radius is and its charge density is given by. To set up an integral which gives the field, you need to represent the position of a section of the ring, and you decide to use the angle between the section and the x axis to do it. Phys Test Y. Kubota March 3, 997 n the CT (Cathode ay Tube) of a color T, electrons, which are generated by an electron gun nearly at rest, are accelerated by an electric field which is created by a pair of electrodes. The electrodes are 5 cm apart, and one of them carries positive charges, whose density is C/m 2 and the other carries negative charges of the same density. (This is accomplished by applying about of voltage on the electrodes.) (a) Assuming that the field between the electrodes is approximately that of infinite parallel plates, calculate the field. (20 points) (b) Assuming that the electrons do not have any kinetic energy before they are accelerated by the electrodes, calculate their kinetic energy and speed after they are accelerated. (20 points) (a) What is r? (3 points) 2. n the hydrogen atom, the electron is circulating around the proton at a radius of m. (b) What is the relation between dl' and d? (5 points) (a) What is the centripetal force on the electron? (5 points) (c) Express r' in terms of. (5 points) (b) What is the frequency of circulation? f this frequency equals that of the light which would be emitted by the hydrogen atom, what is the wave length? s it in the visible (400 to 700 nm)? Or (>700 nm) or U (<400 nm)? (20 points) (d) What is (r')? (2 points) (e) Set up the integral for E(r). (5 points) (g) Show that E y = 0. (for extra credit of 5 points). A cube consisting of 2 wires, six of which have resistance and the other six have 2, is put across a line with voltage as shown at right. What is the current flowing out of the battery? Group test Group test 3 2. A 000-turn thin current loop is placed in a uniform magnetic field of 0. T, and can rotate as in the figure at right. The loop is 5 cm by 5 cm square in shape, its mass is 20 grams, and carries a current of ma. When it is pushed by a small angle from its stable equilibrium position, what is the oscillation angular frequency? 2 2 Test 2 Some atomic electrons are in elliptical (rather than circular) orbits and their distances to the r nuclei vary over the orbits. When the maximum and minimum distances of an Electron orbit electron in an elliptical orbit are defined to be v v' and r, its speed at the minimum distance from Nucleus q the nucleus is given by v = q 2 2 4πε o m r(+r). (a) Show that when = r (circular orbit) the above expression of the electron speed reduces to a more familiar form: v = q q 2 4πε o mr. (0 points) (b) Calculate the electron speed, v', when it is at the maximum distance away from the nucleus using the (total) energy conservation. (20 points) (c) Calculate the same electron speed (when it is at the maximum distance away from the nucleus) using the angular momentum conservation. (0 points) 2. The battery of your car was discharged because you left its room lights on for several hours. After an AAA person gave you a jump start, you were told that driving around for a few hours (day time) will charge up the battery. You wonder if this is true even when head alter lights are on since it was getting dark. You found out from a car manual that () The alternator of the car effectively works as a = 0.06 Ω =5 battery =2 Accessories P = 480 W Head lights P = 36 W each 5- battery with 0.06 Ω internal resistance; (2) each of the two head lights is rated 36 W (for 2 ); (3) during a day-time operation (without the headlights on), the accessories still draws 480 W of power; and (4) it takes two hours to charge up the battery during day time. How long will it take to charge up the battery at night (with the head lights on). (35 points) Test 3

2 . The mass spectrometer is an instrument which is used to measure the masses of ions. An ion of mass M and charge q is produced at a source S and is accelerated by a potential. t enters a region with a magnetic field. t hits a photographic plate at x as shown in the diagram. a. Find an expression for x in terms of the variables given. b. When chlorine of masses 35 and 37 u (atomic mass units) enter, what is their difference in x? Assume that = 00, = 0. T, q = C, and u = Kg. 2. A long wire along the z axis carries a current of S x Photographic plate 0.5 A. A square current loop is located in the xz plane carrying 2 A of current, and its corners are at (x, z) = (0.3, 0), (0.3, 0.), (0.4, 0.), and (0.4, 0), all in cm. Calculate the net force on the current loop including its direction. Final exam. You have a job working with new types of batteries. The chemical solution you are studying contains molecules which consist of charges of +e and e separated by a distance 2a (dipole). The solution also contains ions which are atoms with a charge of +e. You need to calculate the potential due to the dipole that is experienced by the ion. Assume that the dipole is located along the x axis and centered at the origin with the positive side at x = +a, and negative side at x = a. The ion is also on the x axis at x = +D. Simplify the answer by assuming further that D» a. 2. n a research project, you are going to use the circuit at right, but you worry that the power dissipation in the 3-Ω resistor would be too large. The 3-Ω resistor you happen to have can dissipate up to 2 W. Determine if it is adequate. 3. n the course of designing a Nuclear Physics experiment, you need to turn a beam of protons whose speed is m/s through 90. The protons enter a hole in a plate at 45 angle and must exit through another hole 2.2 m away as shown. Two schemes are proposed: one is to use a uniform electric field to deflect the protons; and the other is to use a uniform magnetic field. To help decide which to use, you are asked to calculate the values of the electric and magnetic fields. 4. You have a summer job working for a small company which tries to develop new products. You need a method to take a voltage obtained from a battery and to raise it up to a higher value. You recall your study of capacitors and decide to try out an idea. You build a parallel-plate capacitor with one plate fixed and the other arranged so that by pulling a lever, you can increase the gap between the plates. The plates are 0. 2 in area, and the gap is.0 mm wide. You connect your capacitor to a battery which supplies 9.0, and then disconnect the battery. You now use the lever to increase the gap to 3.0 mm. d. Calculate the work you do in pulling the plates apart. 5. You have just received and installed a large magnet for an M (Magnetic esonance maging) system. The magnet poles are vertical, and the magnetic field between the poles is horizontal. While you are waiting for the delivery of a Hall-probe to measure the field, you need to make an approximate measurement to determine if the magnet is acceptable. You decide to make up a rectangular loop of copper wire of width W and length L (L > W). You will then hold the loop with the long sides vertical. t is partially in the magnetic field so that the top of the loop is in the field, and the bottom of the loop is just below the poles and thus in zero field. You predict that if you let the loop fall, it will accelerate downward for a while, and then fall at uniform speed v. You measure the mass M and resistance of the loop. With this loop, a stop watch and a meter stick, you can make a decent, measurement of the field. Determine the magnetic field in terms of L, W, M,, g, and v. 6. To estimate the electric field due to a 00,000- power line, you decide to calculate the electric field from line charge. For simplicity, you assume that the power line runs horizontally along the x axis from x = 50 m to x = 50 m. You have figured out that 00,000- line has a linear charge density of C/m. Calculate the electric field vector at a point 30 m directly below the midpoint (on the z axis at z = 30 m). One or more of the L 0 following definite integrals may be useful: dx a 2 +x 2 /2 = ln a2 +L2 +L a 2, ( ) L 0 \i(0,l,\f(dx,a 2 +x 2 )) = \f(,a) tan - \f(l,a), \i(0,l, x dx a 2 +x 2) = ln(a 2[ 2 +L 2 ) lna 2 ] \i(0,l,\f(dx,\b\bc\((a 2 +x 2 ) 3/2 )) = \f(,a 2 ) \f(l,\r(l 2 +a 2 )), \i(0,l x dx, a 2 +x 2 3/2) = a 2 +L 2 /2 + L. ( ) ( ) x dx a 2 +x 2 /2 = a2 +L 2 L, ( ) a. What will happen to the amount of charge on each plate of the capacitor? b. Calculate the new voltage after you increase the gap. Note that the capacitance of a parallel plate capacitor is given by C = A o d. c. Calculate the energy stored in your capacitor before and after the increase in gap.

3 MC test. A µc charge is 50 cm away from a charge q and the force exerted by the charge q is N. When the distance increases to m, the force will be (a) N. (b) N. (c) N. (d) 0-3 N. (e) N. 2. A µc charge is 50 cm away from a charge q and the force exerted by the charge q is N. When the charge increases from q to 2q, the force will be (a) N. (b) N. (c) N. (d) 0-3 N. (e) N. e) 4πε o Q 3 L 2+ 4 d A small light conducting sphere is hung still by a string. t is electrically neutral. When a Teflon rod, which is electrically charged negatively, comes close to the sphere a) the sphere will not move since it is electrically neutral. b) the sphere will move toward the Teflon rod. c) the sphere will move away from the Teflon rod. d) whether the sphere moves toward or away from the rod depends on the amount of charges on the rod. e) whether the sphere moves toward or away from the rod depends on the mass of the sphere. 8. The Teflon rod above touches the small light conducting 3. A µc charge is 50 cm away from a charge q and the force exerted by the charge q is sphere. At that instance, N. When the charges change from q to 2q and µc to 0.5 µc, the force will be a) the sphere will not move. (a) N. (b) N. (c) N. (d) 0-3 N. (e) b) the sphere will stick to the Teflon rod due to electric attraction N. c) the sphere will move away from the Teflon rod due to electric repulsion. d) whether the sphere sticks to the rod or moves away 4. An oil drop with a positive charge is moving upward at a constant velocity between two oppositely charged plates. Q =q Q =q P 2 d d * L Q =q 3 from it depends on the amount of charges on the rod. e) whether the sphere moves toward or away from the rod depends on the mass of the sphere. a) The upward force on the oil drop by the plates is equal to the downward force of gravity and air drag. b) the amount of upward force on the oil drop by the plates is equal to that of the 9. A small light conducting sphere is hung still by a string. t is electrically positive. When a downward force of gravity. Teflon rod, which is electrically charged negatively, comes close to the sphere c) the upward force on the oil drop by the plates is less than the downward force of a) the sphere will not move. gravity. b) the sphere will move toward the Teflon rod since it is electrically positive. d) there are no forces exerted on the oil drop. c) the sphere will move away from the Teflon rod. e) the upward force on the oil drop by the plates is greater than the downward force due to the combined effects of air drag and the force of gravity. 5. Three equal charges q are located at three corners of a square. Which statement about the electric field E at the fourth corner (at *) is true? * d) whether the sphere moves toward or away from the rod depends on the relative amounts of charges on the sphere and the rod. e) whether the sphere moves toward or away from the rod depends on the mass of the sphere. a) E is parallel to one edge of the square. 0. The Teflon rod above touches the small light conducting sphere. At that instance, b) E is parallel to a diagonal of the square. q q a) the sphere will not move. c) E is zero. b) the sphere will stick to the Teflon rod due to electric attraction. d) E is proportional to q 2. c) the sphere will move away from the Teflon rod due to electric repulsion. e) None of the above q d) whether the sphere sticks to the rod or moves away from it depends on the amount of charges on the rod. E here e) whether the sphere moves toward or away from the rod depends on the mass of the 6. Three equal charges, Q, Q 2, Q 3, are at the corners of an equilateral sphere. triangle as shown. Point P (at *) is at the midpoint of the line between Q and Q 2. The magnitude of the electric field at P is: a) zero. Q b) 3 4πε o L 2. a) a. b) b. c) Q 3 4πε o L 2+ 2 d 2. c) c. d) d. e) e. d) Q 3 4πε o L 2+ 4 d 2.. There are two electric charges as shown at right. The electric force on the charge Q >0 at * in the figure is represented by vector, 2. f q 2 is +C instead in the above problem, the force vector is represented by a q =+2C b Q* e c q =-C 2 d

4 a) a. uniform electric field E o, which is in the +y direction. After a time t, the y position will b) b. change by c) d) c. d. a) v o t. (b) (/2)v o t. (c) (qe o /m)t. (d) (qe o /m)t 2. (e) (qe o /2m)t 2. e) e. 3. There are two charges as shown at right. Provided that electric field lines appear as shown in the same picture, a) Q 2 = Q. b) Q 2 = 2Q. c) Q 2 = Q. d) Q 2 = 2Q. e) Q 2 = (/2)Q. 4. There are two charges as shown at right. Provided that electric field lines appear as shown in the same picture, Q Q 2 8. A charged particle of charge q, mass m and velocity v o in the +x direction enters a region with a uniform electric field E o, which is in the +x direction. After a time t, the momentum will change by a) qe o t. (b) (qe o /2)t. (c) (qe o /m)t. (d) (qe o /m)t 2. (e) (qe o /2m)t A charged particle of charge q, mass m and velocity v o in the +x direction enters a region with a uniform electric field E o, which is in the +y direction. After a time t, the momentum in the y direction, p y, will change by a) qe o t. (b) (qe o /2)t. (c) (qe o /m)t. (d) (qe o /m)t 2. (e) (qe o /2m)t A charged particle of charge q, mass m and velocity v o in the +x direction enters a region with a uniform electric field E o, which is in the +x direction. After a distance x o, the kinetic energy will change by a) Q 2 = Q. b) Q 2 = 2Q. c) Q 2 = Q. 2. There are two charges of the same magnitude and opposite d) Q 2 = 2Q. e) Q 2 = (/2)Q. 5. There are two charges as shown at right. Provided that electric field lines appear as shown in the same picture, a) qe o x. (b) (qe o /2)x. (c) (qe o /m)x. (d) (qe o /m)x 2. (e) (qe o /2m)x 2. signs m apart as shown at right. The electric field at the mid-point is N/C. The direction of the field at P, 50 cm to the right of the positive charge on the line connecting the two charges, is (a) to left. (b) to right. (c) down. (d) up. (e) toward +q. E=? * P 2 -q +q P * * E= N/C a) Q 2 = Q. 22. n the above problem, the magnitude of the field at P is b) Q 2 = 2Q. (a) N/C. (b) 0.5 N/C. (c) 0.45 N/C. (d) 0.55 N/C. (e) 0 N/C. c) Q 2 = Q. d) Q 2 = 2Q. 23. The same charge configuration as above and the electric field at the mid-point is still e) Q N/C. The direction of the field at P Q 2, 50 cm away from the midpoint in the direction 2 = (/2)Q. Q2 perpendicular to the line connecting the two charges, is (a) to left. (b) to right. (c) down. (d) up. (e) toward +q. E=? 6. There are two charges as shown at right. Provided that electric field lines appear as shown in the same picture, a) Q 2 = Q. b) Q 2 = 2Q. c) Q 2 = (/2)Q. d) Q 2 = 2Q. e) Q 2 = (/2)Q. Q Q n the above problem, the magnitude of the field at P 2 is (a) N/C. (b) 0.7 N/C. (c) 0.5 N/C. (d) 0.35 N/C. (e) 0.25 N/C. 7. A charged particle of charge q, mass m and velocity v o in the +x direction enters a region with a

5 MC test 2 (d) Two C-charges are separated by. When their distance is shortened to m, the potential energy of (e) the charges due to their electrostatic force changes by m 7. 2, the voltage across 2 in the circuit at right, is (a) J. q = C q = C (a).5. (b) 2.. (c) 3. (d) (b) J (c) J. (e) 6. (d) J. 8., the voltage of the battery in the circuit at right, is (e) Two C-charges are separated by. One of them is fixed while the other is moved by 2 m along the arc centered at the first charge. The potential energy of the charges due to their electrostatic force changes by (a).5. (b) 3. (c) 4.5. (d) 6. (e) , the current through 2 in the circuit at right, is (a) J. (a).5 A. (b) 2. A. (c) 3 A. (d) 4.2 A. (b) J. (e) 6 A. (c) J. 0., the voltage of the battery in the circuit at right, is (d) J. (e) n the previous question, the moving charge is moved further after the move along the arc: it is now moved towards the fixed charge by 2 m. The potential energy of the charges due to their electrostatic force changes by (a).5. (b) 3. (c) 4.5. (d) 6. (e) 9. 2 m. A lithium nucleus with a charge of 3e and a mass of 7 amu (atomic mass units), and an alpha particle with a charge of 2e and a mass of 4 amu are at rest. Which of the following methods could be used to accelerate them to the same kinetic energy? 2 m along arc =Ω q = C = 3 q = C 2 =2Ω 2 (a) J. (b) J. (a) Accelerate them through the same electrical = 3 A (c) J. potential difference. =Ω (b) Accelerate the alpha particle through volts and =2Ω (d) J. the lithium nucleus through (2/3) volts. (e) 0. (c) Accelerate the alpha particle through volts and the lithium nucleus through (7/4) volts. 4. Two C-charges of opposite sign ( C and C) are A (d) Accelerate the alpha particle through volts and the lithium nucleus through separated by. The C-charge is fixed while C- (4/2) volts. charge is moving in the direction perpendicular to the line (e) None of the above will work. connecting the two charges (v). One second later, the C moving charge is located away from the fixed charge 2. A negatively charged particle q is released from rest in the uniform field between two D in the directions 45 from the previous position as seen by oppositely charged parallel metal plates, A and, with a potential difference of 45 the fixed charge. The direction of the velocity of the between them. The particle moves toward plate. moving charge is (a) As q moves, it gains electrical potential energy. (a) A. (b). (c) C. (d) D. (e) not enough information to tell. 5. n the above question, the magnitude of the velocity will be q = C q = - C (a) v. (b) 3 v. (c) 3 v. (d) (/3) v. (e) (/ 3) v. (a). (b) 2. v (b) Plate is at a higher potential than plate A. (c) q moves in the direction of the electric field. (d) The path of q is perpendicular to the electric field lines. (e) Plate A is at a higher potential than plate. 3. The same potential difference is applied across two wires. Wire A carries twice the current of wire. f the resistance of wire is, the resistance of wire A is 2 m along arc q = C q = C 6. There are 0.5 C-charge and C charge, which are separated by. The electric potential (c) /2. due to C-charge at the place where 0.5 C is located is (d) 4. (a) 0 9. (e) /4. (b) 0 9. q = C q = 0.5 C 4. Two wires of the same material and cross-sectional area have different lengths. Wire A is three times as long as wire. f the resistance of wire is, then the resistance of wire A (c) E. potential here is 2

6 (a). (b) 3. (c) /3. (d) 9. (e) /9. 5. A potential difference of 20 produces a current of 8.0 A in the heating element of a (a) = 2 = 3 toaster. The resistance of this heating element is (b) + 2 = 3 (a) Ω. (c) (d) > 2 = 3 < 2 < 3 (e) t is impossible to tell without knowing the voltage of the battery and the resistance of the bulbs. 2. Three identical bulbs are connected to a battery, as shown in the diagram at right. Which of the following statements is true about the relative size of the current at points, 2 and 3? (b) 5 Ω. (e) > 2 > 3 (c) 960 Ω. (d) 67 Ω. 22. When a 00 W-light bulb (a bulb which consumes 00W of power when connected to ) (e) 30 Ω. 6. f the power dissipated in a resistive circuit element is P, what is the power dissipated in the (a) the same. same circuit element if it carries three times the current? (b) half as much. (c) twice. (a) P. (d) 2 as much. (b) 3P. (e) / 2 as much. (c) P/3. (d) 9P. (e) P/9. 7. Two resistors are connected in parallel across the same potential difference. The resistance of A is twice that of. f the current through A is, then the current through is (a). (b) 2. (c) /2. (d) 4. (e) /4. Questions 8-20 refer to the circuit at right, which shows three bulbs connected to a battery. 8. f the bulbs are identical, which bulb glows the brightest? (a) ulb A (b) ulb (c) ulb C (d) The bulbs will all glow with the same brightness. (e) t is impossible to tell without knowing the voltage of the battery and the resistance of the bulbs. 9. f the bulbs are identical, at which point in the circuit will the current be the smallest? (a) Point (b) Point 2 (c) Point 3 (d) Point 4 (e) The current will the same everywhere in the circuit. 20. Suppose that bulb A has a larger resistance than bulb, and bulb has a larger resistance than bulb C. Which bulb will glow the brightest? (a) ulb A (b) ulb (c) ulb C (d) The bulbs will all glow with the same brightness. and 50 W-light bulb are connected in series as depicted at right, the brightness (power consumption) of the 00 W-bulb compared to that of the 50 W-bulb is 00 W 50 W

7 MC test 3 7. A dipole is located between two (infinitely large) parallel charged flat. A dipole is located between two (infinitely large) parallel charged flat plates oriented as shown. The dipole experiences plates as shown. The dipole pointing exactly perpendicular the plates +q +q -q experiences (b) (a) a force toward the +Q plate. a force toward the -Q plate. (a) a force toward the +Q plate. (c) a torque into the paper. (b) a force toward the -Q plate. (d) a torque out of the paper. -q (c) a torque into the paper. (e) neither a net force nor a net torque. +Q -Q (e) neither a net force nor a net torque. +Q -Q 8. The electric field inside a spherically symmetric infinitely thin shell of charge Q>0 (d) a torque out of the paper. 2. A particle of mass m and charge q is located at a point in space P near an irregular charge (a) is greater than the electric field outside of the shell. distribution of total charge Q. The force on q is measured to be F. Which quantities are (b) varies as the distance from the center of the shell. sufficient to completely determine the electric field at P produced by the charge distribution (c) varies as the inverse of distance from the center of the shell squared. Q. (d) is always equal to the electric field at the surface of the shell. (a) F and q (e) is zero. (b) F and Q (c) Q and q 9. The electric potential inside a spherically symmetric shell of charge Q>0 (d) The average distance between P and the distribution. (e) q, Q, and the distance from P to the geometric center of the distribution. (a) is greater than the electric potential just outside of the shell. (b) varies as the distance from the center of the shell. 3. A charge +Q is located inside a Styrofoam ball of radius. The net electric flux at the (c) varies as the inverse of distance from the center of the shell. (d) is always equal to the electric potential at the surface of the shell. surface is Φ net. What is the magnitude of the net electric flux at surface if the charge inside (e) is zero. the ball is doubled and the radius of the ball is tripled? 0. The magnitude of the electric potential inside a solid spherical conductor with a charge Q>0 (a) Φ net. (b) 2Φ (a) is greater than the electric potential outside of the sphere. net. (b) varies as the distance from the center of the sphere. (c) (9/2)Φ net. (c) varies as the inverse of distance from the center of the sphere. (d) (2/9)Φ net. (d) is always equal to the electric potential at the surface of the sphere. (e) (4/9)Φ net. (e) is zero. A spherical balloon of radius 40 cm carries an electric charge of -5.0 x 0-7 C distributed uniformly over its surface. There is no charge inside the balloon. The next 3 questions refer to this situation.. A positively charged particle moves in the positive x direction in a uniform magnetic field directed into the paper as shown in the diagram. The resultant force on the particle can be made zero by introducing a uniform electric field of the appropriate strength in the +y + v 4. The surface charge density is: (a) +y direction. (a) x 0-7 C/m 2 (b) - y direction. (b) -.6 x 0-2 C 2 /m 2 (c) +z direction. (c) -.9 x 0-6 C/m 3 (d) - z direction. (e) none of the above. (d) x 0-3 C 2 /m +x (e) - 3. x 0-6 C/m 2 2. An alpha particle, of mass 4 (.66 x 0-27 kg) and charge +2 (.6 x 0-9 C), is moving at 5. The magnitude of the electric field 45 cm from the center of the balloon is: (a) 0 N/C (b) 2.2 x 0 4 N/C (a) zero. (c).8 x 0 6 N/C (b) 5.3 x 0-4 N. (d) 2.8 x 0 5 N/C (c) 3.3 x 0 5 N. (e).0 x 0 4 N/C (d) 2.7 x 0-4 N. (e) none of the above. 6. The magnitude of the electric field at a distance of 35 cm from the center of the balloon is: (a) 3.7 x 0 4 N/C (b) 4. x 0-6 N/C (c) 3.6 x 0 5 N/C (d).3 x 0 4 N/C (e) 0 N/C right angles to a magnetic field of 0.27 T with a speed of 6.5 x 0 5 m/s. The force acting on this particle is 3. A proton with a charge of +e is moving with a velocity v at 50 o to the direction of a magnetic field. The component of the resulting force on the proton in the direction of is (a) ev sin 50 o cos 50 o. (b) ev cos 50 o. (c) ev sin 50 o.

8 (d) zero. 20. n the above, the voltage across the 0.25-F capacitor is (e) none of the above. (a) 0.5. (b) The triangular circuit in the figure is in a uniform magnetic (c) 8. field as shown. The current in the circuit is 0 A and the magnetic field strength is 0.50 T. The net force on the (d) 0. circuit is:.2 cm 45 (e) 50. (a).7 N. (b) 0.33 N. (c) 0.06 N. (a) 0.5. (b) 2. (d) N. (c) 8. (e) zero. (d) 0. (e) At the equator, the earth's magnetic field is nearly horizontal, has a magnitude of about T and points from south towards north. What is the force that it produces on a power line that is 500 m long and carries 00 A in a direction that is 45 east of north? (a) 0.24 N. (b).0 N (c).8 N. (d) 2.5 N. (e) 27 N. 6. When a charged particle moves through a uniform magnetic field 2. n the above, the voltage across the.0-f capacitor is 22. An isolated 0.5-F capacitor is being charged up by a constant current and the voltage across it increased by 5 in 2 second. The current is (a).25 A. (b) 2.5 A. (c) 5 A. (d) 0 A. (e) 50 A. (a) it speeds up. (b) it slows down. MC part of final exam (c) its speed doesn't change. (d) Whether it speeds up, slows down, or remains the same depends on the direction it is. A µc charge is m away from a charge q and the force exerted by the charge q is moving with respect to the magnetic field N. When the charges change from q to 0.5q and µc to 4 µc, the force will be (e) Whether it speeds up, slows down, or remains the same depends on the sign of its charge, the direction of its motion and the direction of the magnetic field. a) N. (b) N. (c) N. (d) 0-3 N. (e) N. 7. An isolated 0.5-F capacitor has been charged up to 0. When it is connected to a 5-Ω resistor, the heat produced in the resistor is 2. Three equal charges q are located at three corners of a square. Which statement about the electric field E at the fourth corner (at *) is true? (a) 50 J. (b) 25 J. a) E is parallel to one edge of the square. (c) 20 J. b) E is parallel to a diagonal of the square. q q (d) 2.5 J. c) E is zero. (e) 0 J. d) E is proportional to q A 0.25-F capacitor has been charged up to 0. The amount of charges on each of the e) None of the above q plates of the capacitor is E here (a) 40 C. 3. Three equal charges, Q, Q 2, Q 3, are at the corners of an equilateral (b) 25 C. triangle as shown. Point P (at *) is at the midpoint of the line between (c) 2.5 C. Q and Q 2. The magnitude of the electric potential at P is: (d) C. a) zero. Q =q Q =q (e) 0.25 C. P 2 q b) d d 9. An isolated 0.25-F capacitor has been charged up to 0. Another capacitor of.0 F is 4πε L o * L then connected in parallel. The amount of charges on each of the plates of the 0.25-F capacitor is c) q 4πε o L +2 d (a) 2.5 C. Q =q 3 d) q (b) 2.0 C. 4πε o L 2+ 4 (c) 0.5 C. d 2 (d) 0.2 C. (e) 0.25 C. e) q 4πε o L 2+ d 2. *

9 4. There are two electric charges as shown at right. The a) Φ net. b electric force on the charge Q >0 at * in the figure is b) 2Φ net. represented by vector, c c) (9/2)Φ net. a) a. a d) (2/9)Φ net. b) b. e) (4/9)Φ net. c) c. d) d. Q* d A spherical balloon of radius 40 cm carries an electric charge of -5.0 x 0-7 C distributed e) e. e uniformly over its surface. There is no charge inside the balloon. The next 2 questions refer to this situation. 5. 2, the voltage across 2 in the circuit at right, is a).5. (b) 2.. (c) 3. (d) 4.2. (e) 6. q =+2C =Ω 2=2Ω q =-C 2 = 3 6. A lithium nucleus with a charge of 3e and a mass of 7 amu (atomic mass units), and an alpha particle with a charge of 2e and a mass of 4 amu are at rest. Which of the following methods could be used to accelerate them to the same kinetic energy? a) Accelerate them through the same electrical potential difference. b) Accelerate the alpha particle through volts and the lithium nucleus through (2/3) volts. c) Accelerate the alpha particle through volts and the lithium nucleus through (7/4) volts. d) Accelerate the alpha particle through volts and the lithium nucleus through (4/2) volts. e) None of the above will work. 7. The same potential difference is applied across two wires. Wire A carries twice the current of wire. f the resistance of wire is, the resistance of wire A is a). b) 2. c) /2. d) 4. e) /4. 8. Three identical bulbs are connected to a battery, as shown in the diagram at right. Which of the following statements is true about the relative size of the current at points, 2 and 3? a) = 2 = 3 b) + 2 = The magnitude of the electric field 45 cm from the center of the balloon is: a) 0 N/C b) 2.2 x 0 4 N/C c).8 x 0 6 N/C d) 2.8 x 0 5 N/C e).0 x 0 4 N/C. The magnitude of the electric field at a distance of 35 cm from the center of the balloon is: a) 3.7 x 0 4 N/C b) 4. x 0-6 N/C c) 3.6 x 0 5 N/C d).3 x 0 4 N/C e) 0 N/C 2. A positively charged particle moves in the positive x direction in a uniform magnetic field directed into the paper as shown in the diagram. The resultant force on the particle can be made zero by introducing a uniform electric field of the appropriate strength in the a) +y direction. b) - y direction. c) +z direction. d) - z direction. e) none of the above. 3. The tsquare circuit in the figure is in a uniform magnetic field as shown. The current in the circuit is 0 A and the magnetic field strength is 0.50 T. The net force on the circuit is: a).7 N. b) 0.33 N. c) 0.06 N. d) N. e) zero. d) < 2 < 3 a) 0.5 N. c) > 2 = 3 e) > 2 > 3 b) 0.6 N c). N. 9. A charge +Q is located inside a Styrofoam ball of radius. The net electric flux at the surface is Φ net. What is the magnitude of the net electric flux at surface if the charge inside the ball is doubled and the radius of the ball is tripled? =0.5T +y + v.2 cm =0A 4. At the equator, the earth's magnetic field is nearly horizontal, has a magnitude of about T and points from south towards north. What is the force that it produces on a power line that is 500 m long and carries 00 A in a direction that is 45 east of north? d).5 N. e) 6 N. 5. When a charged particle moves through a uniform magnetic field +x

10 a) it speeds up. b) it slows down. c) its speed doesn't change. d) Whether it speeds up, slows down, or remains the same depends on the direction it is moving with respect to the magnetic field. e) Whether it speeds up, slows down, or remains the same depends on the sign of its charge, the direction of its motion and the direction of the magnetic field. 6. Two parallel wires carry currents and 2 = 2 in the same direction. How do the magnitudes of the two forces, F, on wire one, and F 2, on wire two, compare a) F = F 2. b) F = 2F 2. c) 2F = F 2. d) F = 4F 2. e) 4F = F Two wires lie in the plane of the paper and carry equal currents in the same direction as shown. At a point midway between the wires, the magnetic field is a) into the page. b) out of the page. c) toward the top or bottom of the page. d) toward the left or right of the page. e) zero. 8. An electron's velocity is along the direction of the magnetic field. The force on the electron is a) in the direction of the velocity. b) opposite to the direction of the velocity. c) perpendicular to the velocitys. d) radial. e) zero. 9. What is the direction of the magnetic field 2.0 cm from a long straight wire carrying a current out of the paper? d. nitially a current flows in the counter-clockwise direction but after the direction of the field changes, the current direction changes, too. e. No current will flow. 22. A wire loop in the plane of the paper is in a magnetic field pointing toward the right. The field is decreasing and eventually points in the opposite direction. a. A current always flows in the clockwise direction. b. A current always flows in the counter-clockwise direction. c. nitially a current flows in the clockwise direction but after the direction of the field changes, the current direction changes, too. d. nitially a current flows in the counter-clockwise direction but after the direction of the field changes, the current direction changes, too. e. No current will flow. 23. A magnetic field exists in the middle part of a wire loop. The direction of the field is into the page, and its magnitude is decreasing and eventually points in the direction out of the page. a. A current always flows in the clockwise direction. b. A current always flows in the counter-clockwise direction. c. nitially a current flows in the clockwise direction but after the direction of the field changes, the current direction changes, too. d. nitially a current flows in the counter-clockwise direction but after the direction of the field changes, the current direction changes, too. e. No current will flow. 24. A current loop is in a magnetic field. The field is into the page, and its magnitude is higher at left than the right part of the loop. The net force on the loop due to the magnetic field a. points left. b. points right. c. points up. d. points down. e. is zero. a) n the same direction as the current. 25. n the above question, the net torque on the loop b) n the opposite direction to the current. c) n the counterclockwise direction in the plane of the paper. a. points left. d) n the clockwise direction in the plane of the paper. b. points right. e) None of the above. c. points up. d. points down. 20. The north pole of a bar magnet at rest with respect to a collection of charged objects also at rest (a) attracts the positive electric charges. (b) repels the positive electric charges. (c) deflects the positive electric charges at right angles to the magnetic field. (d) has no effect on the electric charges. (e) not enough information is given to select from the above answers. e. is zero. large small 2. A wire loop is in a magnetic field pointing into the page. The field is decreasing and eventually points in the opposite direction. a. A current always flows in the clockwise direction. b. A current always flows in the counter-clockwise direction. c. nitially a current flows in the clockwise direction but after the direction of the field changes, the current direction changes, too. loop

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