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Unformatted text preview: PH 132 Exam 3 Spring 2003 Student Name 5 OLA)?! O M 3 Student Number La'ofRecitation Section Number (11,...,35)
Instructions: 1. Fill out all the information above. Write your name on each page.
2. Clearly indicate your ﬁnal answers for all multiplechoice questions in the space provided. 3. Present neat and orderly solutions to each problem. Clearly indicate your method of solution
by including equations used for each part. Final answers should be circled or bored. 4. Be sure to include appropriate units with all answers. \J 5. Permittivity of free space: so = 8.85 x 10—12 Permeability of free space: #0 = 1.26 X 10—6 Multiple Choiceuw Problem 1 Problem 2 Total Multiple Choice (2 pts. each) 1) A closed rectangular loop of wire is formed with ﬂexible wires and placed in a uniform
gagnetic ﬁeld, as shown. The magnetic ﬁeld is directed into the page and is perpendicular
to the plane of the loop. Ifthe rectangular loop resides in a frictionless environment, then when a current I ﬂows in the clockwise digetion, the loop will
8 __h f2=f£x5 7?? z/ﬁxg zﬂBAL‘OO 3 O A) ﬂip over and bunch together; F: B) ﬂip over and spread out into a circle; C) ﬂip over and remain rectangular; D) not ﬂip over but bunch together; E) not ﬂip over but spread out into a circle;
P) not ﬂip over but remain rectangular. Answer 5 2) A wire is formed into a shape that mimics four sides of a pentagon. Each side has length L. The wire carries a current I from point a to point I) and resides in a tactical mmp ﬁeldz
directed to the leﬁ as shown. The direction of the netforce acting on this wire is A) into the page; B) out of the page; C) upward and to the right;
D) downward and to the left. Answer A 3) You conduct several experiments in which you send a proton (m = 1.67r x 10—27 kg) into a aniform magnetic ﬁeld, with its velocity vector perpendicular to the direction of the ﬁeld.
Each time, you change the strength of the magnetic ﬁeld and observe the radius of the
proton’s circular trajectory. The veiocity is always the same. On a graph you plot the radius (r) of the trajectory versus the inverse of the ﬁeld’s magnitude (3*! ) , as shown. From your
graph, you verify that the speed of the proton was N012:
.. r —
?£_ {woesano" _ : 1 : : : F ' E)
s” " 5 " I) 023 ’ ' ' ' swan:
.— 0.6 ...
3 2H0 7mq— 0.4 : 50w: raR v".
0.2 0 l t I i I _
o 1.0 2.0 3.0 4.0 5.0 B;1 (T4)
A) 12 mis;
B) 19 mis;
C) 26 mfs;
D) 52 mis. Answer B
4) A positive charge (+q) moves with velocity (it) through a region of space where a uniform electric ﬁeid is directed into the page and a uniform magnetic ﬁeld is directed to the right.
This particle will experience no net force if the velocity vector has a magnitude of: A) v = E / B and points in the positive ydirection;
B) v = E/ B and points in the negative ydirection;
C) v = B/ E and points in the positive ydirection; Answer 3 D) V = B/ E and points in the negative y—direction. 5) The ﬁgure below shows three circuits consisting of concentric circular arcs (either quarter, Q half, or threequarter circles of radii r and Zr) and radial lengths. The circuits carry the some current. Rank them according to the magnitude of the magnetic ﬁeld produced at the center
of curvature (the dot), greatest ﬁrst. a b c
A) a, b, c;
B) a, c, b;
C) b, a, c;
D) b, c, a; E) c, a, b;
F) c, b, a. . ___ _/:_ Answer Sixteen long paraliel wires carry equal currents I in the directions shown. Rank the
Ampedan loops (labeled a through (1) according to the magnitude of til5"  d3 along each, greatest ﬁrst. The wn'es are drawn in crosssection. %3. as = H 1.5%
Act0 _,_.. I Aim6L" 3"
.Tfzuc. 5 = 0
J1me 4 = J.
fine; .2 2.2.. A)¢hmm B) a, d, c, 13; C)¢amm D) a, b, d, 0. Answer B Evaluate the magnitude of 533 0 d5" for the square Amperian loop (shown as a dotted line) of side 1J2, located inside a wire with a square crosssection of side L and carrying a current I.
Assume the current is uniformly distributed across the crosssection of the wire. A) 211101,
B) ref/2;
C) ﬂOI/4,
D) 4;:0I Answer C 8) The magnetic ﬁeld outside of an inﬁnitely long ideal solenoid (carrying a constant current): A) decreases in the radial direction; B) increases in the radial direction;
C) is constant in the radial direction;
D) is inﬁnite; E) is zero. Answer g 9) A closed conducting triangular loop is pulled away from a uniform magnetic ﬁeld (directed out of the page), as shown. The boundary of the magnetic ﬁeld is shown with a dotted line.
Which of the following is true? 3 o
I O
—r
B o 0
OUT
9 o
O I A) 1(1) 3 I T in time and the induced current is clockwise;
B) [(1) Bl T in time and the induced current is counterclockwise;
C) lfl) 8 Jr in time and the induced current is ciockwise; D) ltl) Bl Jr in time and the induced current is counterclockwise; Answer D 10) Consider a circuit with an emf applied to a resistor (with resistance R) and a capacitor
(with capacitance C) connected in series. The “time constant” for this circuit is RC, which represents the time it takes the current in the ci uit to d ase .I _ a
“4’ M A) zero. " B) approximately 37% of its initial value; “’95”: Tat C) approximately 63% of its initial value; i : Q 0 3 > D) approximately 73% of its initial value; 3 ( 7 Answer B Problem 1 Two long straight wires of length L are parallel to each other and carry equal currents of
magnitudes I in opposite directions (as shown in crosssection). Each wire has a mass m and is supported by a string of length d. The wires hang in equilibrium and the mass of each string is negligible. Use appropriate unit vector notation according to the reference frame given.
Y M __
 a) Find an expression for the magne reforce F B acting on the leftmost wire due to the rightmost wire. (5 pts.) b) Draw and label all forces acting on the leftmost wire.
Find a simpliﬁed expression for the separation distance X between the wires.
Assume that 9 is so small that tam? can be replaced by Sint9 . (10 pts.) c) Evaluate the separation distance and magneticforce for the following values:
I =1_.00><102 A, d = 1.0 m, L =1.0 m, and mg=l.0 N. (2 pts.) (1) An extemal uniform magnetic ﬁeld E is turned on in the positive ydirection.
Find a new expression for the net magnetic force acting on the leftmost wire. (3 pts.) BONUS: Evaluate the new separation distance from part d if the external ﬁeld has a magnitude
of 5610 1.1T (approximately equivalent to the earth’s magnetic field near the surface). M .
2___ ZAILBX #231371. ’X “*3 zvawg sat/E @uAbiAWc. gag Lag VALuES' GWEM'. ‘2— x _. (5),on —(o.c9037’) :O x': 0.5)! I («.mchV41""?qu3 :: 0.06? :0 Problem 2 A circular conducting ring is made to expand in a unifonn magnetic ﬁeld 3’ . The ﬁeld is
directed out of the page and oriented perpendicular to the plane of the ring. The radius of the ring increases linearly with time as r(t) = are + a: i , where r0 is the initial radius and a is a
positive parameter describing the growth rate. 0 t a) Find expressions for the area, the magnetic ﬂux, and the magnitude of the induced emf in the
ring, as ﬁinctions of time. (10 pts.) b) Sketch a plot of the magnitude of the induced emf on the graph above.
Find the initial emf 80 at t.‘ =08 if B = 0.12 T, r0 =10 cm, and a =0.01mfs. (5 pts.) c) Find the current through the ring and the power dissipated by the ring at i = 5.0 s . Assume the resistance in the ring is 0.18 1119. Indicate whether the current is clockwise or
connierciockwise. (5 pts.) BONUS: As the ring expands in circumference, it grows thinner, but the vlu e o t e wire
alwazs remains the same. Find an expression for the resistance of the wire as a function of time, in terms of the resistivity p , the initial diameter of the wire d a , the initial radiusof the ring r0 , and the parameter a: . (3 pts.) ...
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