FINAL EXAM - Astronomywoolf/2220_paolo/2014_exf.pdf · FINAL EXAM PLEASE FILL IN THE INFORMATION BELOW Name (printed): Name (signed): ... Physics 220 Spring 2014 Paolo Gondolo Final

FINAL EXAM

PLEASE FILL IN THE INFORMATION BELOW

Name (printed):

Name (signed):

Student ID Number U __ __ __ __ __ __ __

Discussion Instructor: Anthony KC Matt Paul Peter

Seat #

Physics 2220 Spring 2014 Paolo Gondolo

Important! You are not required to answer all questions in this exam. You will receive points toward your exam points for every question correctly answered. Partial credit is available, however a minimum amount of work and explanation must be shown to receive any credit (for example, a mere list of equations with no explanation of their connection to the problem will not receive credit).

Data: Use these constants (where it states, for example, 1 ft, the 1 is exact for significant figure purposes). 1 ft = 12 in (exact) 1 m = 3.28 ft

1 mile = 5280 ft (exact)

1 hour = 3600 sec = 60 min (exact)

1 day = 24 hr (exact)

gearth = 9.80 m/s2 = 32.2 ft/s2

gmoon = 1.67 m/s2 = 5.48 ft/s2

1 year = 365.25 days

1 kg = 0.0685 slug

1 N = 0.225 pound

1 horsepower = 550 ft⋅pounds/s (exact)

Mearth = 5.98 × 1024 kg

Rearth = 6.38 × 103 km

Msun = 1.99 × 1030 kg

Rsun = 6.96 × 108 m

Mmoon = 7.35 × 1022 kg

Rmoon = 1.74 × 103 km

G = 6.67 × 10-11 N⋅m2/kg2

k = 8.99 × 109 N⋅m2/C2

εo = 8.85 × 10-12 C2/(N·m2)

eelectron charge = -1.60 × 10-19 C

melectron = 9.11 × 10-31 kg

μo = 4π × 10-7 T⋅m/A (exact)

N(Avogadro's No.) = 6.02 × 1023 atoms/gm⋅mole

= 6.02 × 1026 atoms/kg⋅mole

1 Tesla = 10,000 gauss (exact)

ρ(H2O) = 1000 kg/m3

cos(a ± b) = cos a cos b ∓ a sin b

sin(a ± b) = sin a cos b ± sin b

mproton = 1.67 × 10−27 kg

h = 6.64 × 10-34 J

π = 3.14

c = 3.00 × 108 m/s

32 2 2 21x x a dx x a

3

3 2 2 22 2

dx x

a x ax a

ax ax1e dx e

a

3/2 2 22 2

xdx 1

x ax a

2 2

2 2

xdxa x

a x

2 2

2 2

dxn x x a

x a

2 2

2 2

dx 1 a x an

a xx x a

2 2

2 2

xdxx a

x a

1 1

2 2

dx x xsin , or cos

a aa x

dx 1n a bx

a bx b

2dx 1

b a bxa bx


Physics 2220 Fall 2009 Name: __________________________________

Unid: ___________________________________

Discussion TA: ___________________________

Show all work!! Report all numbers to three (3) significant figures. A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal sphere. A typical classroom-demonstration model has a diameter of 30 cm. (a) [10 pts.] How much charge is needed on the sphere for its potential to be 500 kV? (b) [10 pts.] What is the electric field strength just inside and just outside the surface of the sphere when it is charged

to 500 kV?


Final Exam 1


Unid: ___________________________________

Discussion TA: ___________________________

Show all work!! Report all numbers to three (3) significant figures. A proton (charge 1.602 × 10-19 C) is fired with a speed of 1.0 × 106 m/s through the 10 μF parallel-plate capacitor shown in the figure. The voltage across the plates of the capacitor is 50 kV, and the distance between the plates is 10 cm. (a) [10 pts.] Find the magnitude of the electric field between the

capacitor’s plates. (b) [10 pts.] Find the electric force on the proton inside the capacitor. (c) [10 pts.] What magnetic field, both magnitude and direction, must

be applied to allow the proton to pass through the capacitor with no change in speed or direction?


Final Exam 2


Unid: ___________________________________

Discussion TA: ___________________________

Show all work!! Report all numbers to three (3) significant figures. The switch in the circuit shown in the figure has been closed for a long time. (a) [10 pts.] What is the current in each leg of the circuit? (b) [10 pts.] When the switch is opened, the current in the inductor drops by a

factor of 2 in 8 μs. What is the value of the inductance?


Final Exam 3


Unid: ___________________________________

Discussion TA: ___________________________

Show all work!! Report all numbers to three (3) significant figures. The figure is a cross section through three long wires with linear mass density 50.0 g/cm. They each carry the same current I in the directions shown. The lower wires are 4.00 cm apart and are attached to a table. The upper wire “floats” so as to form an equilateral triangle with the lower wires. (a) [10 pts.] What current I allows the upper wire to “float”? (b) [10 pts.] What are the magnitude and direction of the magnetic field vector due to

the lower wires at the location of the upper wire?


Final Exam 4


Unid: ___________________________________

Discussion TA: ___________________________

Show all work!! Report all numbers to three (3) significant figures. A method to measure inductance is to connect the inductor in series with a known capacitance C, a known resistance R, an AC ammeter, and a variable-frequency signal generator. The frequency of the signal generator is varied and the emf rms is kept constant until the current I is maximum. (a) [10 pts.] If C = 10 μF, rms = 10 V, R = 100 Ω, and I is maximum at the frequency f = 800 Hz, what is the

inductance L? (b) [10 pts.] What is the electric power dissipated in the circuit when I is maximum?


Final Exam 5


Unid: ___________________________________

Discussion TA: ___________________________

Show all work!! Report all numbers to three (3) significant figures. An object located 100 cm from a concave spherical mirror forms a real image 75 cm from the mirror. (a) [10 pts.] Find the focal length of the concave mirror (including its sign). The mirror is now turned around so that its convex side faces the object. The mirror is moved so that the image is now 35 cm behind the mirror. (b) [10 pts.] How far was the mirror moved? Was it moved toward or away from the object? (c) [10 pts.] Sketch a principal ray diagram for the object and the convex mirror after it is moved. Be as accurate as

you can.


Final Exam 6


Unid: ___________________________________

Discussion TA: ___________________________

Show all work!! Report all numbers to three (3) significant figures. A positive charge +Q = 4.0 nC is located at x = -a, where a = 0.20 m. (a) [10 pts.] A second equal positive charge +Q is brought from infinity to x = +a. What is the change of electric

potential energy of the second charge? (b) [10 pts.] With the two equal positive point charges at x = -a and x = +a, a third charge –Q is brought from

infinity to the origin. What is the change of electric potential energy of the third charge?


Final Exam 7


Unid: ___________________________________

Discussion TA: ___________________________

Show all work!! Report all numbers to three (3) significant figures. A 10 cm by 5 cm rectangular loop with resistance 2.5 Ω is pulled through a 20 cm by 20 cm region of uniform magnetic field B = 1.7 T (see figure) with constant speed v = 2.4 cm/s. The front of the loop enters the region of the magnetic field at time t = 0. (a) [10 pts.] Find and graph the magnetic flux through the moving loop

as a function of time from t = 0 to t = 16 s (let a flux out of the page be positive).

(b) [10 pts.] Find and graph the induced current in the moving loop as a function of time from t = 0 to t = 16 s (let a counterclockwise current be positive).


Final Exam 8


Unid: ___________________________________

Discussion TA: ___________________________

Show all work!! Report all numbers to three (3) significant figures. [10 pts.] The figure is a graph of the light intensity on a screen behind a double slit. The slit spacing is 0.20 mm and the screen is 2.0 m behind the slits. What is the wavelength (in nm) of the light?


Final Exam 9


Unid: ___________________________________

Discussion TA: ___________________________

Show all work!! Report all numbers to three (3) significant figures. A laser beam of small but finite radius r passes through a thin diverging lens with a focal length of -10 cm. The laser beam’s axis is on the principal axis of the lens.

(a) [10 pts.] At what distance past the lens has the laser beam’s intensity decreased by a factor of 4? (b) [10 pts.] At what distance past the lens has the laser beam’s electric field strength decreased by a factor of 4?


Final Exam 10


Unid: ___________________________________

Discussion TA: ___________________________

Show all work!! Report all numbers to three (3) significant figures. The figure shows a circular current loop near a wire, carrying currents of 0.20 A and 2.0 A, respectively, in the directions indicated. (a) [10 pts.] What is the magnitude and direction of the torque on the

current loop? (b) [10 pts.] What is the loop’s orientation that minimizes the loop

energy in the magnetic field of the wire? Specify the counterclockwise angle from the upward vertical (dashed line in the figure).


Final Exam 11


Unid: ___________________________________

Discussion TA: ___________________________

Show all work!! Report all numbers to three (3) significant figures. [10 pts.] A charge of 2 μC is 20 cm above the center of a square of side length 40 cm. Find the electric flux through the square. (Hint: Do not integrate.)


Final Exam 12

Ph~sics 2220 Sp.-in:,: 2014 Paolo Condolo

.. ,AA,.; '-fY' Name: '1 /V " ~ /

Unid: -------------------------------Discussion T A: · yb o e7 .. j

Final Exam 1 Show all work!! Report all numbers to three (3) significant figures.

A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal sphere. A typical classroom-demonstration model has a diameter o~30 cr11.

(a [10 pts. How much charge is needed on the sphere for its potential to be 500 kV? (b) [I 0 pts.] What is the electric field strength just inside and just outside the surface of the sphere when it is charged

to 500 kV?

v f = -I~

v = Q

~ 0 - 4,, L f v.:

' • 10

Cl S

J>h~ sin 22211 Spring 21114 Paolo Condolo

Name:

Unid: ----------------- Final Exam 2 Discussion TA: __________ _

Show all work!! Report all numbers to three (3) significant figures.

A proton (charge 1.602 x 10'19 C) is fired with a speed of 1.0 x 106 m/s through the 10 J-lF parallel-plate capacitor shown in the figure. The voltage across the plates of the capacitor is 50 kV, and the distance between the plates is 10 em.

(a)

(b) (c)

q

C)

[ 10 pts. Find the magnitude of the electric field between the capacitor's plates. [ 10 pts.] Find the electric force on the proton inside the capacitor. [ 10 pts. What magnetic field, both magnitude and direction, must be applied to allow the proton to pass through the capacitor with no change in speed or direction?

\ . ' I [. (,~ \j - j -

[.:. ~v ("'. ) J() ·' () --J , I 1M

\1

-r~,( ' ' I ! lA"l,-',.:-fM t/~cir,t:

::: 5:x /05 v/u, ,----------------" ......... -

q_v.B-;..q_[

5 := Ejl/

\ J -\' (,. . -C>f s )< ;0 5 -"'l~

-i'-1 t1l f. 0 i xiO _-', -------------------

.:! /e ( fv- ,z_ f~ru ...

/'.4/1./ J 0 )

o (~ po.·"~r :~ ; llfv po...a_::... _\ ___________ J

,---· I s r· I •

~-----~-~ .. ~-- •.... ,~·-"'

Name: _ ___1_:_.::: _______ _

Unid: ----------

Discussion TA: --------Final Exam

Slaow all work!! Reoort all numbers to three (3) significant figures.

The switch in the circuit shown in the figure has been closed for a long time.

(a) [10 pts.] What is the current in each leg of the circuit? (b) [10 pts.] When the switch is opened, the current in the inductor drops by a 5.0 kQ

factor of2 in 8 J.IS. What is the value ofthe inductance?

(a-) Afte-r ll- '""'(5 . f-r..-e.- ~ C- v< fir ~:1-- • \

~tdy -> ~;:: D "" ~I '1$.

12 v

s

L

S·i'-"~~ po~t..,•a..R Jrlf ~r-o?S ~ 1"k~ ""-r· ., ;> •

A\i = L ~ = L~o = o

- b. t. = t..

Pln-.it' ~~'0 Sprin~ 201-l Paolo Condolo

Name: Pa. 11 I Unid: ------------

Discussion TA: ........ ~--------Final Exam

Slacm all work!! Reoort all numbers to three (3) significant figures.

The figure is a cross section through three long wires with linear mass density 50.0 g/cm. They each carry the same current I in the directions shown. The lower wires are 4.00 em r,. l( c-. apart and are attached to a table. The upper wire "floats" so as to form an equilateral triangle with the lower wires.

(a) [10 pts.] What current I allows the upper wire to "float"? I, (b) [1 0 pts.] What are the magnitude and direction of the magnetic field vector due to ~

the lower wires at the location of the upper wire?

4 /

r , 4.0cm

b) J..8 ~o5/ Jo") ::--+ 2

)Jo,X ~~ll) -rr r_;

. "f(/~ ~''tf*tl 11 I!JfC~ T --

- 'LO IT -f - <. -·'(()

~

Ph~ sics 2211 Spring 21114 Paolo Gondolo

Name: ___ f_~~fc~r __________________ _

Discussion T A: ---------------------Final Exam 5 Unid: ---------------------------


A method to measure inductance is to connect the inductor in series with a known capacitance C, a known resistance R, an AC ammeter, and a variable-frequency signal generator. The frequency of the signal generator is varied and the emf Enns is kept constant until the current I is maximum.

(a) [I 0 pts.] If C = I 0 j..lF, Erms = I 0 V, R = 100 Q, and I is maximum at the frequency f = 800 Hz, what is the inductance L?

(b) [10 pts.] What is the electric power dissipated in the circuit when I is maximum?

(o..)

... \.

(b)

c

/..,p,.lahce.' z,l R.2

+

~at,..;:.-::::) ~ I ' z"ils :: rce => L=-

(?.nf)~ c

L )_:: ~.'lb rnH J

C!i!H.S

e~e.Hs. I/CHs EteHS • p = = z

P=

=0

-.3 :: 3,q6xlO J-1

E~s-· CA:Ns

;::

~

I

Ph~ sks 220 Spring 2014 Paolo Gondolo

Name: ----~r~~~r ______________ __

Discussion T A: -----------------------Final Exam 6 Unid: -----------------------------


An object located 100 em from a concave spherical mirror forms a real image 75 em from the mirror.

(a) [10 pts. Find the focal length of the concave mirror (including its sign).

The mirror is now turned around so that its convex side faces the object. The mirror is moved so that the image is now 35 em behind the mirror.

(b) [ 10 pts. How far was the mirror moved? Was it moved toward or away from the object? (c) [10 pts.] Sketch a principal ray diagram for the object and the convex mirror after it is moved. Be as accurate as

you can.

~- --·- ----1-------

t:r::::. lOO c-..

(b) _]_- ---

l~ !>

(!''

(c..)

__ [ ____ _

..l t- J.:::. fY i. f

-+ loo o-.

#OO.xtS

IOO+ "T 5'

I -

tr.:. 100 (...l't'\1

i :::.+-=15 c.~

·I l =- 35 c.nv

I - + 0""' L

.,:: cl ' 42d'5c.ANv ;r .f=-f-=-- .

cr'=r c- 35) ,1( C- 4 z .d's)~ l'fo. 9 C. \f)\

(-~s')- (-~'2.cfs)

=> (Acr):= o--'- rY =·~ ~ .. ,..,. • ..,. 1\ WAY.'

q 0. 'I C/l1'u

:;~ ----- 11 ~ - -· :::-'"' - -

r c.

Ph~ sics 220 Spring 2014 Paolo (;ondolo

~/115 L"'=./' Name:---------~~~----~~--~-~--------

Discussion T A: -·-~--+-''-'-"'-<-':....;"'-'-'"'=-;;, __________ _ Final Exam 7 Unid: -----------------------------


A positive charge +Q = 4.0 nC is located at x = -a, where a= 0.20 m.

(a) [ 10 pts. A second equal positive charge +Q is brought from infinity to x =+a. What is the change of electric potential energy of the second charge?

(b) [ 10 pts. With the two equal positive point charges at x = -a and x = +a, a third charge -Q is brought from infinity to the origin. What is the change of electric potential energy of the third charge?

a. () ::

- Q

'hr €.

::

+Q

-a

-Q +Q

0 a

Name: kC..... Unid: · K f.\( Final Exam Discussion TA: ----------

Slao!f all work!! Reoort all numbers to three (3) significant figures.

A 10 em by 5 em rectangular loop with resistance 2.5 n is pulled through a 20 em by 20 em region of uniform magnetic field B = 1.7 T (see figure) with constant speed v = 2.4 em/s. The front of the loop enters the region of the magnetic field at time t = 0.

(a)

(b)

[1 0 pts.] Find and graph the magnetic flux through the ,moving loop as a function oftime from t = 0 tot= 16 s (let a flux out of the page be positive). [1 0 pts.] Find and graph the induced current in the moving loop as a function of time from t = 0 tot= 16 s (let a counterclockwise current be positive).

-.:-

---1

4.t~! '

"-'

4 ~~ 'tl))')

I

l\

)~c;- lb

sai i.

8 "' 20cm ..,

• • • 8•

• • v • •

• • • •

t '; J.t<.c..l., ~i .... <:<- t: cl/v tO 1 t-1/

:: /~4t.J4/)

~ Li./t..G... l.,

·-"\ 1,ot.-l·t0 V

Name: t£N Unid: -----------

Discussion TA: Final Exam

~----------

SilO!! all work!! Beport all numbers to three (3) significant figures.

10 pts.] The figure is a graph of the light intensity on a screen behind a double slit. The slit spacing is 0.20 mm and the screen is 2.0 m behind the slits. What is the wavelength (in nm) of the light?

. ,1-.

Intensity (mW/m2)

12

~10\/ -5 \ (o, ~ ~PAAJ\. o, Z.o ~to &A-1. J

z.,olY\-

9

Ph~sil's 2211 Spring 2014 Paolo Gondolo

Name: fVI.., f-__

Unid: _____________ _ Final Exam 10 Discussion TA: __________ _


A laser beam of small but finite radius r passes through a thin diverging lens with a focal length of -10 em. The laser beam's axis is on the principal axis ofthe lens.

(a) [I 0 pts.] At what distance past the lens has the laser beam's intensity decreased by a factor of 4? (d c 1"\

(b) [I 0 pts.] At what distance past the lens has the laser beam's electric field strength decreased by a factor of 4? ~ o 1 ,.....

13 e... "' ; "u.m .'Yl _j "-' , p « .. t/ e I r "·'( CA. II j_'vif~l--- -frot<'\ ·iocA..! po: 11.--b

:r po-_v :::!.

pc)W'e...r .=. _::...- ....:-----

&Cr fA- 17 y- t..

5.> v/~ .1" I 7T (' 1..

r-~Y - ..... -:Lc, - 'i - R?.. Jr.\...

'X --i

I (,_!0 -07_ '-( :::

)( -1/Q ! t til , .. ., :....,...

-------------------------------

b)~ _f ,'5 prt->por-t~rmtc, i fo IE/1.. So wh~ r: _L =.

I£ i -z. £:0 '1

); I I

>olv-e. llc.. ...--- ~ ~ ...--. PLI"ld k Sq,_, L lr ... (It, e._ - 16 !A/tty 'J:b I £c. I J.. f~c-J.·o ~ 4~_ tt~"c~s.

(;I o )c >( ~ '30LJ'f1 ,~~ IJ,(_ Je,~ --- ::.;-;w ~ lt

Name: 1\ G Unid: ----4==-\L~E~'----Discussion TA: ~---------

Final Exam 11 SilO!! all work!! Reoort all numben to three (3) significant figures.

The figure shows a circular current loop near a wire, carrying currents of0.20 A and 2.0 A, respectively, in the directions indicated.

(a)

(b)

[10 pts.] What is the magnitude and direction ofthe torque on the current ·loop? [10 pts. What is the loop's orientation that minimizes the loop energy in the magnetic field of the wire? Specify the counterclockwise angle from the upward vertical (dashed line in the figure).

- -------1!1 ~ 2.0cm _

®--Wire 2.0A

~ 12t+R IA rrr J,

~J-A) (n (.odt~)">-) (:-9.)

b,J-~· lb1 (-9-) --

-----····-·······

t ~ (Co/2~·to.,)[;;l·to) (-:9. ]<.~) ::: f LJ.~~tou -7_

~-tk ,->

-z,e.rU ~ ~ ~~ ~ vdhuJ,

·~ j2.0mm JAO.zPA

or · C.loc/t-ll)t_

rvh..~C>f\

~'Jf'..J" )A-

l'h' '.Jl' .' .'tl Sprin~ :!0 1-l Paolo Condolo

Name: f u._ u J Unid:

------------~---------

Discussion TA: ---------------Final Exam

Sian all work.!! Beoort all numbers to three (3) significant figures.

12 [10 pts.] A charge of2 J.LC is 20 em above the center of a square of side length 40 em. Find the electric flux through the square. (Hint: Do not integrate.)

~ Lt1r!ar 2

6--<--<6, tO-d 11 (t)-f<

Documents

FINAL EXAM - Astronomywoolf/2220_paolo/2014_exf.pdf · FINAL EXAM PLEASE FILL IN THE INFORMATION BELOW Name (printed): Name (signed): ... Physics 220 Spring 2014 Paolo Gondolo Final