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Unformatted text preview: November 29, 2004 Physics 1322 3rd Hour Quiz  Benbrook Name: Easy Stuff  2 points per problem. Show work in space provided. / 1. Two line circuits carry currents [1 and 12 around space curves 01 and 62 . Write
Ampere’s Force Law for the force on circuit 1 due to circuit 2. 7: : Z11 M J’QXCMLV;:3 31 a
C
m 2.;‘Write the Biot—Savart Law for circuit 1 of the previous problem. (’yl‘x/ (La N
3((7'r’3
6%, ”"11 ML — ll
,ﬁé/S Iran” L6 v/ 3. Write the Lorentz Force for a charge q moving in ﬁelds E and g with velocity 17 . . F ; q (€150 X€§ %
75?},4. For the case of a charge q moving in a uniform magnetic ﬁeld E , what is the name
‘ that. describes the trajectory of the charge? ?\ . ta '2! 5. If the charge of the previous problem has mass m and is moving with its velocity 17
perpendicular to the magnetic ﬁeld, what is the radius of the circular orbit followed by the ycharge? MW _ Q
' a: 433;, e \/ 6. What is the angular frequency that describes the motion of the previous problem? .is 2 {h \/,, 7. Given a magnetic ﬁeld E , how would you calculate the force on a circuit c carrying
current I in the ﬁeld? 33,1; Silage; @ / 8. Consider a circuit described by the space curve c carrying current I and write the
equation that you evaluate to calculate its magnetic moment. /
, \/ 9. What is the torque on a dipole ,1? in a magnetic ﬁeld E? ? a N w) p)
, a ,w x15
10. Write Ampere’s Circuital Law. M 11 .. Sins V BL ( 11. Give an approximate expression for the magnetic ﬁeld inside a long solenoid with N
turns, length .l , and cross sectional area A if the current in the winding is I .
$4) 12. What is the self inductance of the solenoid in the previous problem? [A N1 b
L :2
.What is N ewmann s formula for the mutual inductance between two line circuits? Wféfff dﬂ $1:th 14. What is the magnetic energy stored in an inductor L carrying current I ? Ml? (T 15. Give an expression for the displacement current density. a: ”i @Write the four equations that we refer to as Maxwell’s equations (in vector differential
orrn). : [405 + M _’
V” E ’ 0/9, V ’< «P: ‘
1’ _, f’/ 3/8 I
/ 17. Deﬁne magnetic ﬂux é E 66
t it 1/:
31 pa {Mao A
[email protected]:o V34 mt not /— 18. What is the time constant of a series L R circuit?
L R 19. For an ideal transformer with Nm turns in the primary and Nout turns in the
secondary, what is the Output voltage Vow; for an input voltage Vm 7 3.
Vout : FL Viv T”; (1 l 20. If current [out flows in the secondary of the transformer of the previous problem, what
is the current in the primarv? “ /
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.L‘ 5 ’ﬁ f1 A
21. Give expressions for the complex impedance of a resistor R , a capacitor C , and an
inductor L . Zr. '7 {wL . a
1 ' 7W ” ‘2
2Q ’/ ﬁwc 22. Complex impedances “add” like 4%:4 5/0 . El For the next two problems, assume that a plane wave in a medium of refractive index 711
is incident on a plane interface beyond which the index of refraction is 712 . The angle of
incidence is 61 , the reﬂected wave leaves at angle QT , and the transmitted wave leaves
at angle at . 23. What is the relation between 61 and GT ?
Gt 2 95 a
24. What is the relation between 01 and 6t 7
(I, sine; = Yizsmet %
25. What is the mirror equation for a Spherical mirror of radius R ?
a— f 5 : a
26. What is the thin lens equation? 111,1 9\ 27. What is 231/01” the mtensﬁgr behind Young5s double slit? f!\:ti/TTQ Sig/‘11?) .W t ‘s theciégaction intensity behind a single slit of width a illuminat 7d in wave—
at“ an 0 7 1/sz 5/99! {7.4 f 74 T
5 1 :[ ”gala T9146) len 22 fWhat/is the intensmyxbehind a diffraction grating of N slits of width d
fix/T f" 7”” 5 7/ M 7? Z
5 5,.) M 7 5/5 5 i / 3 75512155 // 30. What is the” resolv1ng power of the géting 1n the prev1ous question in or er 5m ? L we ' 7’ _ In“; .15»er /»"f / !,//
5/ If k T ~ 0 ‘ " ///
I g :L I! :3“: y %W/ / ’
, 51 9/
.5“ , ,z' 1"
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5/!“ (5/ // NNWW \Mi WW Hard Stuff Show work on separate sheets provided. 1. Two" circular turns of wire, one of radius R1 and the other of radius R2 , where
R1 «>5 R2 , are Concentric and co—planar. Calculate the mutual inductance between the c mks /, two turns in the approximation that the ﬁeld produced by turn 1 does not vary over the n
area of turn 2. (Neumann7s formula is NOT a good way to do this!) (20 points) 2. A current density 1s described in cylindrical coordinates by ""5 ﬂoSi(1)idi \n, .5..— rr 1*
1:10;? 0<r<a \\2>\ r 04
:0 a<r “W “Wee we Calculate the magnetic ﬁeld in the two regions. (30 points) 7Con51der the AC circuit below.
Find the effective impedance driven by the voltage source. (10 points)
b) Use your answer to determine the amplitude and phase of the current supplied by the source to the circuit. (20 points)
c) Make a crude plot of the current amplitude as a function of u) . (10 points) 9}th / ,
4. wo converging lenses, each of focal length f , are separated by distance 4 f as shown
elow. An object is located 2f in front of the ﬁrst lens. a) Find the location and magniﬁcation of the image formed by the ﬁrst lens. (20 points)
b) Find the location and magnification of the ﬁnal image formed by both lenses. (20
points) 5. A right circular cylindrical tube of radius R , length h , and negligible wall thickness
spins about its axis at angular frequency w. A charge Q is uniformly distributed over the
side wall of the cylinder Calculate the magnetic field at the point on the axis equidistant from the two ends of the cylinder (30 points) /
W / 1r; 4"" Q + m. WEE “2m \ C w: (3+ {guxiiMEnk ’ } ...
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 Spring '10
 MichaelGorman
 Physics

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