Name: Page2

1. Using a dip needle, it is determined that the Earth's magnetic field makes an angle a withrespect to the horizontal plane. Then using a horizontal compass, a circular coil with N turns andradius R is aligned with its plane vertical and its axis perpendicular to the horizontal componentof the Earth's magnetic field. The compass is placed at the center of the coil. Passing a current Ithrough the coil produces a deflection e in the direction of the compass needle.

a) Express the strength BEofthe Earth's magnetic field in terms of the current I, the angles a ande, and the properties of the coil. (lOpts)

~ ~ ~~~BE== 8,x.x + B~; ~L ~ ~

~-tL ~ ~ ~ f£ ~ ~.~ 1J--dY~ ~> b.r-~ ~ ~k,. -~

-::JU ~ ~ Be::= 8~ ~ ~~ ~~ e> t;.,..B~ B,/£.- 1.

~ ~ B~:;: /36 ~o() ~ ~ I3E

~ --~-Vt/ iL ~ Ck)t-iL ~ or; Oc

12 :;:; 6 A/.J- f fiiP- /D tlIv~ '-1-"- (V 9" f<2- -- ~ ~

J-

t<

d&

=8~~# ~~~~t%>

'"f5 -;:::::.£

IV'! /1i>--;;2R

uYff).:.---u-o Ol... -

b) Compute BE assumingN =10, R=10cm, I=0.3A, B=4Y, a=60' (lOpts)-'-I \

g ~ D.377 C- L~ I? =--Jv T J£

Physics 263 Exam 1 Prof JJ Kelly

2. Recall the can-crusher demonstration in which the charge stored by a large capacitor is rapidlydischarged through a conducting band around the middle of a soda can. Suppose that the currentflows in a counterclockwise direction within the plane of this page.

a) Sketch the discharge current and indicate the direction of the magnetic field it produces.

. /. .L.J B <'1. . --/--J 1\/\ (5pts)~ ~ /v-- I ~~ ~ ~

~ ~ -1-, V> @

-'; ~tL~~t0~ q/;: h CC-lJ) i£-F - ?/() I £~ ~~ ~%~~

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b) In what direction is the current induced within the can?

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(5pts), ,

~ I--?-

~ 1;; ;;£~~. ~ ~ a~ I/ / ~

~ ~ ~ 1L~ ,,/B,!4.,I~

~~) ~ 7i5 ~1.

~ ~~ ///Llt3=fl. 1-73~ /:2

d+ ~ ~O! {{2Z- ~~ ~ :;2Lc-

~~ ~z@Z/~

~ ~~. ~.:1=, =-:> ~ -1--'2--=:> ~ ~/:i,.x ~ (~~) i£. c.--

~. ~~. atC;~> ~ -L, ~--L~

~ ;t;- ~ ~ ~4 ~ -;::, ~-= q->.-

~~~£f ~

c) Explain why the can is crushed.

h

(10 pts)

~

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~...L2,-

VrL

Physics 263 Exam 1 Prof JJ Kelly

Name: Page 4

3. A thick metal bar of mass m, length L, and resistance R slides without friction on a pair ofparallel metal rails with negligible resistance. The rod is initially at rest and the switch is closedat t = O. The rails are connected to a battery that provides constant electromotive force &. Auniform magnetic field B is directed perpendicular to the plane of the circuit formed by the rod

and rails. Show that the velocity Ofthe rod as a function of time takes the form v = v"" (1- e-t/r)

and determine v"" and T. (20 pts)

I

[= ($)8 IR

L~.

~F L

1

~~~~:J~ ~~~~~

4Uu4 pt.J

F-== TEfL ~ -(; ~ ~.

V f}L ~ t;L ~J

T ---- 13:- vEL-R

/32-,[2 f!,BL- IJ-:=-mR rJ'7R.)v

yY1 -Itr!!.- 1/ 8'- j J/~ 6L.q -- -t-

f.- tic-::;:::::

f ~ 0 ~/

_-t/-z: )v:::: ~ l/-c:.-

-C -'> c:z> ~ '::-> V---'?~ e~ 0 :;::;=/-/ ) /1:

jv Voa V tBLV--'??0 )

--- -'7 --- ~ ~::::- ::...----tit 1:: 1: n1R..

:. ~ ~: ~~1oft/ v V

~ ~'6~~ fi+i"'"-,2~I - c/r: ) :--. dv v~ _-I-/. ~ ~

V -:::= V l. (- c-- =,..; - ::::: - e /t' +- .-'> #t: 'L h? .

t!Vob :::: . g L

~~~:

/0 ~)

~

Physics 263 Exam 1 Prof JJ Kelly

Name: Page 5

4a) Two long perpendicular wires carrying equal currents cross, as shown, but do not quitetouch. Indicate on the diagram the locus of points at which the net magnetic field vanishes andexplain your reasoning. (10pts)

~ -IL /4/L '0 ~ t/u ~ ~ ~ ~ ~(Iv . ~/ ) ~- /I~~ ~~C?-

- -~ -r;;-~ ~ ~ - .;el, '2. 2. 1 2 - J V.~/Vvvv;:~ . , -' d~/ ~~~~ -:;:> x -j C 0:='j +.or -:0> :;- - "'.

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~~~~u> ~ .~

:J-':::::-"'-j ~=O Ltc

.rt~.

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r

""'" ..:::.

"~1! (3-=-0;J:-

b) A particle with mass m, charge q, and velocity v is subject to uniform static electric andmagnetic fields, Eand B. (i) Under what conditions, if any, will the particle remain stationary?(ii) Under what conditions will v remain constant? (10pts)

.> ~ :>.--"-

F / 1,(£-+-1/@13) -== D

......

dt/ - 00 Tt-

;;r; tZ ~.-::>

~~J~

/J ...L.J~ ~.~ ~ . ~~ "~ £ = - " @B. 7'.;.,.. 7/,<.<. ~ ~~ ~ (t:~o\ tv-< ~.~ e~°.J .-?oiC if' ~~ --">. ~ .

~) p iJ c 11" + 1/1. ~ V" h' -'>.

~ ~ z=; B. ;¥£ ~ F;, =()

-> --'- /Jf) B~.-=- £ = t/ B . .7'"J- --tIvc vL~~ ~..E :::::-- \! ICY :-' ' J.. .L ~v~J.-. J- .>~ B

( /f7-b:=.1

cuJ

--vJ..~

Physics 263 Exam 1 Prof JJ Kelly

5. A long cylindrical shell with inner radius a and outer radius b carries total current] along itslength.

a) Find expressions for the magnetic field in the regions (i) r < a, (ii) a < r < b, and (iii) r > b .

Sketch the function B(r) . r - - t - , ~ (10pts)

~1I r B~-==-/D I le-hdoseJ)L! r< a.

L. ) Ir 2 a .zr < b- CA-

£'-a""'- Jj,<..r-

b) Evaluate the pressure assuming that the shell is thin, such that a ::::;b ::::;R. Is the pressureinward or outward? [Hint: consider the force upon a narrow strip of current rmming the length

of the cylinder.] r (5pts)Ad

:2-rr~ 8rj:=:/° I =:>!Sf = :5.rr R.yzL/bF-=::-;;2.7TR

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\

r-

~ I deelF = - :r;L ;;- ==>~TTR

;4 -;; .;(;r R L ~~2-

P 0= ~D (!;R).. ~ ~'I.L

c) Compute the pressure for R =0.3 em and] = 8 A .

P :;:- 0, ~).£ -;;2

Page 6

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~ - _'~.~

L

~(J

(5pts)

Physics 263 Exam J Prof JJ Kelly