8/2/2019 PLTL 6,7,8

1/16

PLTL week 6 E&MConcept: You should review the right hand rule because this section of material is very dependent on the right hand rule. One uses itto detelmine the direction of force on a moving particle in a magnetic field and one also uses it to determine the direction of magneticfield produced by sources. Fill in the table below for practice.

F=q v X BF=ILxB

B = I x r

\ / ~ \ J d o U ~ f3 ~ ~ c

~ ' ! - ; ~ ~

C, ''1",.// v tI- " f ) ~ f ' / / ' \.... rt:1/'J. . V B F

East Into page .JJ 01.-!'IV0 South WestOut of Page SouthW ~ s - r

Jfi-.cI.vf. .. 4 d ~ : ( d 1'1 t ~ f r : ~ v v I + ~ ' t i'.J1-

~ J ; : ~ ~ '---------'

1. A slab of gold 2.00 rum wide and 5.0 rom thick cames a current of7.0 A out ofpage. An external magnetic field of7.0e-5T acts to the right.

a. What is the drift velocity of the charge carriers if n = 5.9 x 1023 e_/m3 (v = I/nqA)?b. What is the magnitude and direction of the magnetic force experienced by the charge carriers?c. What is the electric field set up by the charge can-iers?d. What is the magnitude of the potential difference and which side is high potential?

2. A slab of gold 1.25 mID wide and 4.5 rom thick cames a current of 10.0 A into page. An external magnetic field acts to theright producing a potential difference of9.5 V between the top and bottom ofthe gold slab.a. What is the magnitude and direction ofthe electric field set up by the Hall effect? tJ(jrec;h ~ 1r" 6' eM vJr!y1.:ftJb. What is the drift velocity of the charge carriers ifn = 5.9 x 1028 e-/m3 (v = I/nqA)?c. What is the magnitude oftbe external magnetic field?d. Which side of the slab is at high potential?

3. A He+2 ion has kinetic energy 4.5e-16 J and mass 6.68e-27 kg. I tmoves in a southward magnetic field of5.4e-5 T at anangle of35 degrees E ofS.

a. What is the total velocity of the ion?b. What is the force the magnetic field exerts on the ion?c. What is the radius ofthe path the ion takes?d. What is the period of the circular portion of the i o n ~ motion?e. What is the pitch of the translational portion of the ions motion (the distance between points where the circular

motion repeats itself)?4. A 4.6 C charge has kinetic energy of2800 J and mass of2 g. It is moving to the east. It reaches a region of an electric field

of300 N/C to the east ~ n a magnetic field of 0.7 T vertically upward.a. What is the initial velocity of the charge?b. What is the magnitude and direction of the force due to the electric field on the charge?c. What is the magnitude and direction of the force due to the magnetic field on the charge?d. What is the magnitude and direction of the net force on the charge at the instant it hits the fields?

5. An electron is produced by a source and then accelerated to the north through a region with a potential difference of 87 V.What is the electric field if the region is 0.30 m long?

a. What is the magnitude and direction of the [mal velocity of the electron if it started at rest? , / , Gb. The electron then goes through a region with a magnetic field of 0.002 T directed vertically up (no electric field).

What is the magnitude and direction of force acting on the electron?c. Lastly the electron is in a region with an electric field of 120 N/C to the east and the magnetic field is stiJI present.

What is the magnitude and direction of total force acting on the electron?

8/2/2019 PLTL 6,7,8

2/16

- -

o'

, ()oi YYl

,~ - -

:: f .O A . -::::4-,J..jIS"\O.S'rY\- ('":i.9 I 0 1 . ~ ~ ~ \ - ( l' Ie 'I O ~ \ q 2 ) (. oo?-' ,0 o M) ._- -.

vn ) l'A >ex'vJb) f :: ~ ~ ' - J ' ' \ _ _ _ _ _

( L , ( O I ~ ~ \ ' \ c , ) { : t - ..(.U ' I O - ~ ~ ) - ~ ~ - : O ' O - S ' ' ' t J ~ ~ _ . _ ~ 0 2 j Q - ' l . ! _ __ ~ A _ ( ~ ( 2 -"""-'- - . . . - ' - - - - ~ - c) B-vl3 : r5 .e-

F - v'fS __ _ __ .. _. _;:: T.tfl-S--'JO $ ' ~ _ . 1:0 '10) = ' i r / C f L ' I ( ) - 1 _ ~ u-v-;L

S md) :: E ' = ('),I 'II W"1) -(Pr7':... ) = 2. 'i'1S- '/0 - I I V

e.) ~ ~ # ' h . , ~ ~ 1 : ~ l . i Y t . ~ t - - t .0( d ~ J l . ~ J - . - \ & ~ iJ ' ' - P ~ 1 ~ - j J ~ . J 4 . . t t L ~ A\- -

8/2/2019 PLTL 6,7,8

3/16

8/2/2019 PLTL 6,7,8

4/16

- - -----

PL/L W ~ k - & 'PA _ ~ V E'd.._:0 . ,gf v ~ ,3 YY\

E::: 240 .!;f. _c) \J :::. 0 ( 7 . A . . . ~ A..x =-, 3 YY1F: Iig_ : 2- o,0CZ - ( I&} O ~ I ~ C )

F .::: WI . Of.-.,I.{&1'!O -t=1JJ =(1.. / L . ) O - 3 ~ ~ ~ ' tA

_ ?L- :. _' ) , () 'J 33 ,I ' m-- .$").V ~ VI; '2. t 2 ' p., .bX __ v'-- 1 ) + 2 ( i i . Q ~ 3 3 _ ' I _ Q ( ~ . L i 3 r t t . ) _ - '_'. _ s1. /

.--- - - - - - - - - - - - ~ V ~ 5',_3.'/1 ~ ! U . ' ;10 ? - 1 J ~ ~ _ _ ....S - - - - : - - ~ - - - ' " - - - - I -. -.. .-- b) f:: , v 13_ __I - - - - .- (f.h.'JO'&(5-,SlLO b-rJJ.) {,_Q02 T) _

:: I, t (Pt.](p, . 0 -1'5jJ . .10 5 ' _ : ' - ~ ' ~ ~ ~ ~ I) f: ' 6 ( ~ ~ W l i L ) { I - 2 - 0 1!) '" l ' ! i , ; ~ - ' 7 - AI - " - ~ ' ~

~ ( ! g r P f ~ ~ a - ~ CU- l4 --4 _ : f l - ~ . ~ e . ~ ~ ~ :::fLe ~ t : i : . t - d . . ~ ' d c f l _ ~ ' k ( l , t W ~ f : lrfr-e flu-: (I, 1 - "I&d -/

8/2/2019 PLTL 6,7,8

5/16

PLTL week 7 E&M1. What is the magnitude and direction of the magnetic fields asked for at the point P shown

below ifr = 0.050 m, theta = 0.250 * pi radians, and i = 4.5 A?a. magnetic field fl11 18ft si:4e dtt"e- ft; leff sfn'pb. magnetIc field G H - - ~ ~ d ? l t . . -10 ,rrjl,-r Sfr-tFc. magnetic field on curved. total magnetic field

2. What is the magnitude and direction of the magnetic fields asked for at the point P shownbelow ifri = 0.038 m, ro = 0.068 ill, and i = 8.0 A?

a. magnetic field from topb. magnetic field fi-om bottomc. magnetic field from left & rightd. total magnetic field

3. A long straight wire carries a cun-ent of7A A as shown. A wire loop of8 turns andradius 3.1 m is adjacent to this long straight wire and carries a current of 4.8 A as shown.What is the net magnetic field (magnitude and direction) at the center of the loop if it is adistance of 6.8 m from the long straight wire.

..._.._._ , _.-- - - - - - - - - - - - )

8/2/2019 PLTL 6,7,8

6/16

4. A long straight wire has a current density of 6.4e7 A/m2 The wire's radius is 0.0038 m.a. Using Ampere's law derive an expression for the magnetic field produced by a

wire?b. What is the magnetic field produced by the wire at a point 0.0012 m from the

center of the wire?c. What is the magnetic field produced by the wire at a point 0.0054 i l l from the

center of the wire?

5. A coaxial cable consists of an limer wire ofradius 3nun and an outer metal cylinder ofinner radius 6mm and an outer radius of 8mm. The inner wire has a cunent of6 A out ofthe page and the outer cylinder has a current of 9A into the page.

a. What is the magnetic field (magnitude and direction) at a distance of 3.8 mm fromthe center.

b. What is the magnetic field (magnitude and direction) at a distance of7mm fromthe center?c. What is the magnetic field (magnitude and diJ.ection) at a distance of 8.8 mm from

the center.

)

8/2/2019 PLTL 6,7,8

7/16

__ - - - - - .J .A, . ~ ~ ~ ~ ~ l 4 U ' - 1 f ~ c h -6t.;.;., 1 ~ t f ) p t ! L j ( ) - ~ L 0 - -o d1 t:L ~ c i r c 1 f \ L } , . - 8 ~ c l M , b ! := rd!J-,; r'tP_ _ (1ft" () ~ ~ ) ( g , O k ) Z j ( r ~ ~ L_ - - : ; - ~ t ~ L Q - ~ ~ 0

'!I#-(, 0 f , S ~ . ) - - - - - - -.. ~ . L - 2 _ -....+K" ....

= ( 1 / t / O ~ ) (f{OJf){fiVrJ .f.J-tLl.flo-s-r !:,_- - - - - - - L f L C : ~ ? ~ ) - - - - ~ - o ~ - : - - 4 2 " t - ~ - - - - f . ~ i r n - ? ~ . : J

'6 - " - - -- .-- - _.zbp L ! i ~ ~ I ~ J u + ~ L b . __-lI-- ------t:L&..:i..Pul ,!f) -5 ; - ) (3,.hi0 '/tj'-fj .e j , v q / ~ /O-ST

- - - - - - - - - - - - _ ...- _ .... - ,-- ... _ . . . . .

-"

-

8/2/2019 PLTL 6,7,8

8/16

----- - -

i A . . . . I _ ~ ~ 13 . ~ A g .. () u . ? -vv''O ~ f t . ; . - wiic =- .VIAa ~ - - - - . . :....- ----2tr f

.. .(ytr'io -7) (?- 4/1) 2,IlIP Hr+ ..J21Y (q- ~ g f Y 1 )IJ . - f...-II CI'rt lvfr' ;? 'It t/l.-. ..

f 3 C M - ~ ( , :: -_M{) t '1: __ _c4tp t ' (z-rr r ~ ) ( 8 f;l:;-n4 )- -1 fIv'( 1.tr'tI_ ( ; Y ~ \ ' J ( ) - q ) ( 1 . q A ) ( i f r , . / ~ l ( i ~ - ; ~ I _ ~ : t , + ; ' J b - v - . _ _ __ __ __ _I.!f( 13. /M) __

, -----

8/2/2019 PLTL 6,7,8

9/16

{?J--77-/4JwL 1- 4 ' r t b L _ ~ ~ __._. .- --r -. - - - - - - - - - - . . : . . : - ~ - ~ - = - - - - - - - - : . . : , , - - - ' - - - - ~

- - - - - - - I r - - - - : : : - - - ' L " " ' - . . : . . : ! . ~ ; r - = Y l < ! . C . . l - - - - - - - - - - - - . . . . . : : . ~ - - . - - ' - - - ' - - - - - - - ~ - -- - - - I - ..t..-...J - - - - - - ' - - - - : ; ' r - - - - - - - - - : - ~ - - ; - - ' - , , - - - - - = - - - _ - - - - . : ' : . : . . - . - - - - - - - A a -- ----!aJ (f 2-fry ' = # ~ ~ 1 ~

, I/'I

..--------- -

---------- ..- - - -_ ...

- - - - - r - \-, - -. --~ - -_- _ - = - b ~ / ) ~ : - I 3 - - = , - A o - - ~ - - . -----i---., . . . .--- - - _ ~ ) :2.ff'r;/ ' 1Irt.!: we ~ ~ ( e

d"cird7'/I" -/rr !! t:. - h-.f " ~ " ( - ? ' f ' , 4 ----t:ter. -r-.d..-. --

- ._

- -

-_ . - .----

- - --- - ---- - - -- - - - - '--- - -====- - -

8/2/2019 PLTL 6,7,8

10/16

- - - - - -

---

,PLTL Nlkk +_ &fi _/ u .~ H : 4 -.fL"..;( ~ t ~ - ~ j ~ - - ~ ' { f ~ ~ ~ f tit - 7 ~ _ - & .:fJrp - ~ M Y /tt&:KJ _ - ~ ~ j ; / l - f Yif,

a _ ) _ f f 2 ~ 1 7 ' - ' ' ( ' M v it0L< A'uc.-JaA..' 0 4rvtdl h / " r ~ . ~ -1iv 'Ir) - ; cPA - ~ - - ; j ~ - 2 5 - L / D j ,_

~ - - - ~ -- - - . 2 ~ I eo b g - ? 1 . # ~ ~ ---- - - - - - ' ~ / ; g - ~ ~ I t v - ~ d N ~ / ( ~ ~ V { t ' - y 13 - A A ~ ~ . ? v ~ f (J;t ..A

0 'J / t ~ w t t - v t . M rA-o t./.fJ; -/ ~ ~ : - ~ d;;e (S(J)-vR

8/2/2019 PLTL 6,7,8

11/16----- -

I i - ...1,i-V;-A-@10 ~ If 01-1J.J!e ~ __ _ . ----"-------'..... _.__

. . . . . . . . . . : ~ l ? b I ' t ~ - b - , -- - - ~ - ' . _ - , , - - - ' - - -;Lft!-c --.--------

~ ' - ' - } O ~ - - : 2 I - '-=-t:

8/2/2019 PLTL 6,7,8

12/16

PLTL week 8 E&M

1. A coil of wire with 7 turns is in a solenoid of 200 tUllls/m. The coil has a diameter0.0400 m and the solenoid has diameter of 0.050 m. The current in the solenoid isclockwise and decreases from 10.8 A to 6.0 A in 25 s. The magnetic field is parallel tothe nOlmal of the coil.

a. What is the change of cun-ent divided by the time ofthe solenoid?b. What is the induced emf in the coil?c. What is the direction of the source magnetic field, the induced magnetic field and

induced current?d. What is the induced current in the coil if the resistance is 700 ohms?

2. Consider a rectangular loop ofwire of length of 1.9 m and width of 0.28 m. This loop isin a region ofmagnetic field 0.008 T directed out ofpage. The loop has a velocity of 0.8mls into the region ofB.

a. What is the induced emf in the loop of wire if the wire has 7 turns?b. What is the magnitude and direction of the CUD."ent in the loop if its resistance is0.009 ?

c. What are the Joule heating losses in the wire?d. What is the magnitude and direction ofthe net magnetic force on the wire?

3. A single rectangular loop of length 0.18 m and width 0.20 m is in a magnetic field of 120Tout of the page. The magnetic field is inclined at an angfe of30 degrees to the nonna!of the plane of the loop.

a. If the magnetic field increases to 240 T in 30 s, what is the magnitude of theinduced emf in the loop?

b. If the loop has a resistance of 0.1 ohms, what is the current in the loop?c. What would by the power through the loop?d. If the magnetic field stayed constant at 120 T but the length of the loop decreased

to 0.09 m in 30 S, what is the magnitude and direction of the induced emf in theloop?

4. A long solenoid with 160 turns and length 0.20 m, radius 65 em, and current of 10.0 A isfilled with a magnetic material of relative permeability 60 .a. What is the average magnetic field of the source?b. What is the magnetization?c. What is the total magnetic field?d. What is the field due to the atomic currents?

" " - ' - " - - - " - - ' - " .._--

)

8/2/2019 PLTL 6,7,8

13/16

- - ~ - - - r ----

8/2/2019 PLTL 6,7,8

14/16

If,t}":.!,OjrYJJ :; (), '21IYJ8 .oo't:TGN :=.. 1 - f w t - ~ o

oJ ~ > - f l )J ' r3. . Co () ~ - - t ; tm"" . (, OOH) ( f l 0Y. -e('i y--- I I

~ t ~ ( =: 1 - ~ i d (; oog t-). :/. !. 1M ' 7S!:!:l 0 ~ S - / 2 - V. ( 5'b) V:: l'/Z A 1'/ A-o g 5 ~ c { 1'-.fOg!.) (:2- :; ~ (10 0 9.-0-) :" (3 ft'dPf l LLuCR...J- '" il cit- & t e ~ : K y ~

vi - q , 4i)q-8A ~ 1 'dr [ ) 5t'h,- ' Q..; . WtlAct ~ h f . ,a c 'c.J ~ t . . c / l A ~ . A - r;;/c) f : v' L'

~ ( j < : t r S 7 2 V ' 0;. err-irA.::, '60'SvJ

bL) -F L';t X- 13 .. ~ ._ ' 9. yr18;4 ( e , - t ~ J (t O(/JT) ;: l-. JII f i~ ~ @ r ~ ~ . A 1 > ~ e - . f ; 5 ~ ) Te-f ~ . ( ~ k : ! - ) '

8/2/2019 PLTL 6,7,8

15/16

fLTI- /!Ueelt- 2%Yl f:u 6 ~ Y Y L . 3- - - " ; ' : : : " ' - ~ - - - ' , /' B

.Q:. .1'(

iJ\) V l :: )JA .w ( ) ' ~ J 2 __ ~ t . _ _ . .

I ' ( / ~ r n ',2YY\') . CoS 30_' (210 -/2f) c) '-. q/ 2 ~ V.30x(.h) \{ :::. (' [

8/2/2019 PLTL 6,7,8

16/16

PLTL t1Jftl g)J /10 irvtM t/\.) S s ~ u - - J" f; s ( ) ~ ~ L ; ; : - . A / l ~ ' L' 'ft .--f O,2yrt ::- 111" Jo-: , IOIt . ( / & ~ ( ~ )

.2- yv' ly:;;; &)rn~ ::: /0 1/1- .6 ~ o =- (J. 0 I 00 Tk- ;: J ~ ~ O c.) (, 0 I OQS-T ) ((po ) ()JJpQ3

- C ()-fJJd., . v r u ~ - - & : ( { + O BS6"-A@ _t ' MoM k 6 s ~ c . < , . ,

-) 8 ~ ~ l { -: e ~ - : { 3 s ~ u -=- A o f1Il_,BAt- ::