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Unformatted text preview: March 27; 2006 {Claw  Q .9 Q. 1:. h Physics 1322 211d Hour Quiz  Benbrook Name: Kiwi“ Easy Stuﬁ'  2 points each. Show work in space provided. —1 1. W hat is the torque on a dipole 15’ in an electric ﬁeld E ?
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1;: P.x E 2. ‘Write an equation that we refe; toi as Gauss= Law.
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_ E A dis :g; F U 3. Write an equation”I that we refer to as Ganss’ Divergence Theorem. jgdg 7 :viﬂdv 4. VFhat is the electric ﬁeld at F produced by a dipole ff located at 5'0 ? Al {a r “ﬂurrw‘;£rr“>__ :2“ \ m?
C" ‘ilfﬂo( lf»r".r lC—r‘\3> 5. write out the gradient of )“(X1 Y, Z) : 3XYSZ2 .
Z A '1' .L A s \ '5 I‘ 6. W'rite the position vector F in terms of the spherical coordinates r , 6" , and qt) and
the Cartesian unit vectors 5 , j , and k . (—3 ( '];.':'.=:'.":n: 1 4 ‘ 5"’5*5'\A j‘ 4 [£059 1‘:
7. Compute the divergence of 1301’, Y, Z) : €(X2) + 5(Z3) .
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8. What is the curl of 13 from the previous problem? i _‘ t _1 L \ z r ICE—E}; If £23 H 1‘ ii ‘ L ﬂ —, 3:16. W? ' :— r :L a ) "_ '_r e : \. I'ax'! ...v A: I A:   V1. .2” w u '3 f _
9. Write the positiOn vector 'F' in terms“ of the cylindrical coordinates r , (ii = the Cartesian unit vectors i , j , and I: . .. f
n . r'k. (': 3‘_/, (bag L rig... 10. What is the volume element in cylindrical coordinates? (chr To 11. ‘What is the volume element in spherical coordinates?
(‘1 ‘31“ a Cl( 12. What is the ﬁrst of Maxwell‘s four equations in vector differential notation? _ J5"
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13. What is the deﬁning equation for electric potential.
I =1 #3 , __._._— ﬁnes j [t{(‘\ 14. “That is the deﬁning equation for capacitance? #3.
C'v _. —a 15. What is the relation between the displacement D , the polarization P , and the electric
ﬁeld E ? J 9: £156“? 16. “That is the relation between X3 and the dielectric constant K ?
34 '— l 1' X g 17. ‘Nhat is the energy density associated with the electric ﬁeld? Up. : £9 égk  L
18. \F'Vhat is the deﬁnition of the electric susceptibility XE ?
a J a, x if r ‘ 19. In terms of the polarization P , what is the equivalent volume charge density pm; ? r P"  ax. «
,. 20. the equivalent surface charge density 0pc; ? x.
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21. What is the relation between the current density and the current I ‘? j: €T3,6l3 x... . Write Ohm’s Law for the current density. 10
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23. State thhoﬁ‘s ﬁrst law.
2: I '—' O 24. State Kirchoff‘s second law. 55 =é1’K’ 25. What physical principal is embodied in Kirchoff’s ﬁrst law?
r Ler',;.~(‘Uotl—low 0‘ Clan(€4.9 ..J 26. Given V , the potential drop across a. resistor, and I , the current through it, what is
the power dissipated in the resistor? P 2 I V
27. What is the time constant of the series R — C circuit? vm Hard Stuﬂ — 20 points per problem. Show work on separate sheets of paper. 1. Calculate the effective resistance of the combination of resistors shown below. 3. A portion of the X axis is charged such that the charge per unit length is Speciﬁed by: A :Ao(X/a)2 , X1 <0:
=0 , a <IX Calculate the electric potential at (0, Y) . 4. A volume charge density is Speciﬁed in spherical coordinates by p20 , 0<r<a
=,oc,r2/.:L2 , a < 'r < 2o
:0 , 2a<r Find the electric ﬁeld as a function of r . Malia a sketch of the magnitude of the electric
ﬁeld as a function of r . This is a timed exam; you must stop work at 6:55 PM. Write your name on the top of the
ﬁrst page in the form LAST, First and turn in this copy of the quiz with your additional
pages of work IN CORRECT ORDER! DO NOT fold the papers or insert them inside the quiz. They will be stapled together. :iSRvaﬁﬁﬂio +1—3a;{) Wt) *
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 Spring '10
 MichaelGorman
 Physics, Electric charge, Fundamental physics concepts, charge density

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