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Unformatted text preview: 311)an @oﬂﬂoge
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mam TOTAL MARKS: 100 May 20, 2005
TIME: 3 HOURS 9:30 a.m. to 12:30 pm. This examination is divided into two parts: PART I (30%) — Answer only six (6) out of the seven questions or problems in
this section. Each question or problem is worth 5 %. PART II (70%) — Solve only seven (7) out of the eight problems in this section.
Each problem is worth 10 %. Instructions: 1. Ifyou answer more than 6 questions in Part I, or solve more than 7 problems
in Part 1], indicate which one(s) you want omitted. 2. Formulas and constants are given on the last page of this exam. Expressions
not given on this last page should be derived. 3. Calculators are allowed. 4. You may answer two questions on the same page. However, solve every
problem on a different page. . Write only on the lighthand pages of your booklet. Use the lefthand pages
for your rough work. Show all your work, including diagrams, in the exam booklet.
Give all numerical answers to a threedigit precision.
. Do not tear any page(s) ﬁom the examination booklet. Ifyou use more than one booklet, number your booklet. When you hand
in your examination, place booklet #2, 3, etc., inside booklet #1. 10. Write your name and the name of your teacher on each booklet. Physics NYB Final Exam 1’ May 20, 2005 PART 1 (30%) — Answer only six (6) out of the seven questions or problems in this section. 1. A bar magnet is dropped vertically downward and falls through a conducting loop, as shown in Figure 1. During the magnets entire motion, which of the following statement(s) is correct?
Assume that you are looking downward into the loop. (a) The current in the loop always ﬂows in a clockwise direction. (b) The current in the loop always ﬂows in a counterclockwise
direction. (c) The current in the loop ﬂows ﬁrst in a clockwise, then in a counterclockwise direction. (d) The current in the loop ﬂows ﬁrst in a counterclockwise, then in a clockw1se direction. Figure 1 (e) No current ﬂows in the loop because both ends of the magnet move
through the loop. 2. A circular coil has a cross sectional area lof 0.200 m2 and a resistance of 2.00 9. A uniform magnetic ﬁeld directed perpendicular to the plane of the coil is turned on. Ifthe ﬁeld through
the coil increases linearly from zero to 1.50 T in 50 ms, determine (a) the magnitude of the induced emf in the coil while the ﬁeld is changing, and
(b) the induced current in the coil while the ﬁeld is changing. 3. Draw a diagram showing two long wires, wire 1 and wire 2, separated by a certain distance d
and carrying currents in the same direction. Determine whether the two wires attract or repel each other. Your diagram should include the appropriate magnetic ﬁeld and force vectors to
illustrate your answer. 4. If the net ﬂux through a gaussian surface is zero, which of the following statements are true?
(Note that more than one statement may be true.) (3.) There are no charges inside the surface.
(b) The net charge inside the surface is zero. ‘
(c) The electric ﬁeld is zero everywhere on the surface. (d) The number of electric ﬁeld lines entering the surface equals thenumber leaving the
surface. (e) E  a2 = 0 everywhere on the surface. 5. (a) Reproduce Figure 2 in your exam booklet and add in this diagram a voltmeter connected so as to measure the potential
difference across R}. (b) What should be the resistance of an ideal voltmeter? Why?
Explain what problem(s) may arise if the voltmeter‘s
resistance is not close to this value. Physics NYB Final Exam I May 20, 2005 . 3 6. (a) Suppose that the electric ﬁeld is zero throughout some regiou of space. Can you conclude
that the potential is also zero in this region? Explain.  (b) Suppose that the potential is zero throughout some region of space. Can you conclude that
the electric ﬁeld is also zero in this region? Explain. 7. Figure 3 represents three rectangular loops in a magnetic ﬁeld E. The ﬁgure shows an edge
View of each loop, that is, the plane of each loop is perpendicular to the plane of the page. The
three loops each carry the same current I, with directions as shown in the ﬁgure, and have
equal areas A. (a) Find the net force on each loop.
(b) Find the magnitude of the net torque on each loop. (c) In each case determine whether the torque would rotate the loop clockwise or
counterclockwise. Physics NYE Final Exam / May 20, 2005 4 PART E (70%)  Solve only seven (7) out of the eight problems in this section. 8.A hollow insulating sphere has a uniform charge density p. Its
inner and outer radii are a and b, respectively. See Figure 4. Find
expressions for the magnitude of the electric ﬁeld in the regions (a)r<a,
(b)a<r<b,and
(c)r>b. 9.A uniform magnetic ﬁeld of magnitude 1.50 x 10—3T is
directed along the positive 3: axis. A positron (of charge +3,
and same mass as an electron) moving with a speed of 5.00 x106 m/s enters the ﬁeld along a direction that makes
an angle of 850° with the x axis. See Figure 5. The motion
of the particle is expected to he a helix. Calculate (a) the radius r of the trajectory, (b) the time it takes the positron to make one
revolution, and (b) the pitch p. 10.(a) In the circuit shown in Figure 6, ﬁnd the a C 1332001X 6' currents I; and 12 and the emf 6‘]. State the directions of currents II, I2, and 13. R4=12.OQ (b) Prove, numerically, that the total power
produced in the circuit equals the total power
consumed. Figure 6 11. In the circuit shown in Figure 7, R1 = 6.00 k9, R2 = 18.0 kg, R3 = 12.0 kg, 8 = 12.0 V, and C = 2.00 pF. Suppose that the switch has been closed for a time sufﬁciently long for the
capacitor to become fully charged. (a) Find the steady—state current through each of the three
resistors, (b) Find the charge on the capacitor. Now, at t= 0, the switch is opened. (c) Find the time at which the charge on the capacitor is one
ﬁﬂh Of its original value. Figure 7 ((1) Find the current through the 12.0kQ resistor (R3) at the same time as that of Part (0).
Physics NYB Final Exam / May 20, 2005 5 12. Two long wires a distance d apart carry equal
antiparallel currents I, as shown in Figure 8. Show that E at point P, which is equidistant ﬁom the T J’ wires is given by _‘ .. P
B = 2t;oId 2 i d x
ﬁ(4}i dd ) ‘""”"—___.R‘_‘___"“4
In your derivation, be sure to show every step i
clearly. Figure 8 13. Consider a uniformly charged disk of radius a and charge per unit area (3. Assume that the disk
is perpendicular to the xvaxis (on the y—z—plane) and that its center is at x = 0. (a) Prove that the electric potential at a point P located on the axis of the disk and at a distance x from the center of the disk is given by V = Zukecr N 3c2 + a2 — it].
Show a diagram and clearly explain every step in your derivation. (b) Use the result of Part (a! to ﬁnd an expression for the magnitude of the electric ﬁeld
along the axis of the disk, a distance x ﬁom its center. What is the direction of the
electric ﬁeld? How do you know? 14. Capacitors C1 = 6.00 uF and C2 = 2.00 uF are ﬁrst charged by connecting them in parallel
across a 250—V battery. The capacitors are then disconnected from the battery and hem each
other. They are then connected positive plate to negative plate and negative plate to positive
plate, as shown in Figure 9. Calculate the resulting charge on each capacitor alter the switches are closed.
. G
Figgre 9 rilﬁ _ 51 d (:1 cg" '— —— ++++ bLﬂ/J
. $2 15. (a) Consider a circular wire loop of radius R located in
the y—z—plane and carrying a steady current I, as
shown in Figure 10. Derive an expression for the
magnitude and direction of the magnetic ﬁeld at an
axial point P a distance x from the center of the
loop. Be sure to show a vector diagram to
explain your work. I Z (b) Use the expression you found in Part (a) to
determine the magnetic ﬁeld (magnitude and
direction) at the center of the coil, that is, at x = 0. Physics NYE Final Exam 1 May 20, 2005 6 Auxm a; Mn and PM u. M Em
mum
M. 2005
(d)
(a) s=6.00V; (b)I=3.00A
The two wires attract each other. 03) 311101)
. (a) The voltmeter must be connected in parallel across R1. (13) The resistance of a voltmeter should be very high. Ideally, it should be inﬁnite, so that no
current passes through the voltmeter. U‘PP’P!‘ 6. (a) No. For example, consider the case where four positive point charges, of the same
magnitude, are at the corners of a square. The electric ﬁeld at the center of the square is
zero; however, the electric potential IS not. (b) No. For example, consider the case of two point charges of equal magnitude but opposite signs. The electric potential at the midpoint between the two charges IS zero; however, the
electric ﬁeld is not. 7. (a) The net force on any current loop carrying current in a magnetic ﬁeld is zero. (b) The magnitude of the torque on the leﬁhand loop is 2' = 0; that on the middle loop is
r =IABsin60°g and that on the righthand loop is r =IAB (c) The lefthand loop would not rotate, the middle and the right—hand loop would rotate
clockwise. 3 3
3_ (a')E 0 (b)E=_p___(r__:§g_l_ (C)E=p_(b___c_1_)i 380 r 380 r2
9. (a) r= 1. 89 cm; (b) T=2 38 ><10'B s; (c)p= 1.04 cm
10. (a) £1=12.,0V I1=10.0,A Iz=8.;00A
(b) The power produced in the circuit is PEl = 120 W, and the power consumed is also 120 W. 11. (a) I; = I; = 0.500 mA, 13 = 0; (b) Q; = 18.0 pC; (c) t= 9.66 x10"2 3;
(d) I; = 13 = 60.0 uA, upward through the 12.04;!) resistor. 13. (b) E = 21tk80' [1— x ] . The electric ﬁeld at P is in the positive xdirection. We know I 2 2
x +a
this because the electric potential depends only on x (it is independent of y and z) and E = Ex: m—d—V is positive.
ab: 14. Q1'= 750 pc and Q; = 250 pic 1R2 ~ II.
“'0 121'; (b) B: “’0
2(JR2 +x )3 2R 15 (a) 13’: Physics NYB Final Exam / May 20, 2005 7 ...
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