phy142 exam1 fall11 solns

5/17/2018 Phy142 Exam1 Fall11 Solns

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Physics 142 LAST Name (print)_S~~o~e_'-.,)~-1-___L_'_;_'_O_""-_ ~ _Signature: _

Midterm Exam 1FALL 2011

September 28, 2011FIRST Name (print) _

UIN#: _

PROBLEM POINTS SCORE1 20

2 203 20

4 205 20

Total 100

2

1. Textbooks, cell phones, or any other forms of wireless communication are strictly prohibited in this orany exam. Giving or receiving aid in an examination is cause for dismissal from the University. Anyother violation of academic honesty can have the same effect.

2. Perform the necessary calculations in the space provided. If additional space is needed, use the back ofthe question sheets.3. ALL WORK MUST BE SHOWN IN ORDER TO RECEIVE FULL CREDIT.

4. All answers must include appropriate units.


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1. (20 points) Three charges are arranged as shown. Charges q =+1 f..tCare located at (0.1, 0) and (0, 0), and charge - - - q = -1 f..tCat(-0.1,0). The dimensions are in meters. Usek = - _1_ ~ 1 0 1 0 Nm2/C2

4Jl '&o

y(0,0.1)

a) (6 pts) Calculate the total electric potential at the point (0,0.1).-q q q

(-0.1,0) (D (0.1,0)8 Q)\I(0) a .< ' ) - = - \j\~2_ ~ V '3'f:-~o..\f2\fA

b) (4 pts) Calculate the work required to place a charge Q =+0.01 nC, initially at rest at infinity, atlocation (0, 0.1).

3


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c) (6 pts) Calculate the electric field E (magnitude and direction) at the point (0,0.1) from thethree charges located on the horizontal axis.

_/ ....... _7 -")E~ t : : , - T ~v-\- \:3::: (- \:\51< \,-,S ~ - \, c"s L \ . S ) )k t : . . , _ j I e C . . :~3S\"''-\S~ ~ 'i:3(;>S'-\_S~)

-7\:2Q (O.0.1)

'q(-0.1,0)

C D(0.1,0)o

d) (4 pts) Calculate the net electric force F (magnitude and direction) on the charge Q of part (b)from the other three charges.

-?c h "(e_C~ \.O~ ,,\ '\- " )..

4


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a) (5 pts) the equivalent capacitance of the system.C \" \ \ \ -\ l\\-\~~L3r~.lr ~ j~2 _ \ > - ~ ~ ~ \f-~ j-::.2 Y - ~ A- \ s' \ > - - ~ - = - 3_ '3 Y - -~

~~C3b C'L\_b) (5 pts) the magnitude of the charge on the 4-JlF capacitor.

2. (20 points) For the system of capacitors shown in the figure, find:

2 [If 4 [If

90V

c) (5 pts) the potential difference across the 3-JlF capacitor.

Q3b - = - C3~ ~Q\j - = - 2_ y'\- ~D\I~3-= -

d) (5 pts) the total energy stored by the group of capacitors.

5


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a) (5 pts) What is the total initial energy of the proton? Show that the particlewon't be able to reach the right plate .

. .:::, '.E V l e < t r O : : ~ 1 liz.} 1V ) V : - - / E / X~ a~ J I 1 1 . - 1 ' d J ~" p o iYl+ o xfT~l ~ V = / E I ; t: [ E I J . : ~V :: 250Y

-2~ 'i 2 ,;) 9tVlhj't); ~(I . t - t -2)((o K d )( .2 ' ({oo/5) + (/.6rfO (QC) (250V)-'1-_ " ';':/-: < -l~ __- ? : J - 44"f- ( 0 J -f. .1{ "f.10 J : : - T ~ J . / . I ( " " K I 0 J ,1:+- P ' f ' O i D V l hl POS'S

b) (5 pts) What is the proton's speed as it collides with the negative plate?

-Iq.;;_-'i '7 -1(4 ' f o r D J_z-1.61-2'(-(0 ~d

\ 1 J f ::),q1Y(V'~\6


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c) (5 pts) The distance between the plates is 2mm. Calculate the magnitude of the electric field between theplates. Use it to find the surface charge density on each plate.

f -----_._------

d) (5 pts) What is the value of the electric potential Vat the turning point (where the proton is at rest)? Usethis and the value for E to fmd the turning point, Xf, of the proton.

L 1 ~ : : -Lll{~ - = - C { ( V - I 1 _ )A ~.f- V}

o

. -!:f-." S - J { / f ') C IOJ + a . 50 VJ - b 1{O-IQC 4G5V

---~-

. ., . _ ., .. - - , :- -. -- .- - -. -- ~ - -~ - -- .- -- . . - -- P - -. - . . - -7


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per) =po(1- 4r/3R) for r < Rper) =0 for r > R

4. (20 points) A nonuniform, but spherically symmetric, distribution of charge has a charge density per)given as follows:

where pois a positive constant. (Use the differential volume in a sphere dV = 41[/ dr.)

~ Q 0

b) (6 pts) Apply Gauss's Law to obtain an expression of the electric field in the regions r > R and r < R.


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\L_ ~~--------~------------~>yK f - / c _

c) (5 pts) Plot the radial component of the electric field as a function of r.

d) (5 pts) Find the value of r at which the electric field is maximum.

9


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5. (20 points) A voltmeter is attached to the two terminals ofa usedbattery of unknown internal resistance. Without other connections, thevoltage reading is 9 V. When an external resistor R = 400 Q isconnected to the terminals of the battery, the voltage reading becomes6V.

R

a) (5 pts) Determine the current in the circuit.

b) (6 pts) Determine the internal resistance of the battery. ()

~~~ G:>",~eC:A\"'b ~\e_ , - \QCSL ~S: \ " ''''' \-~~ '-Jc'C~~c.:'C~ .lr\.e... \>~~~~') ,,~ ~V = - C . - j_ "=> ~ - = - t:. - ~ V ~ - ~ 5 1 - ~ LC)CJ _ 5 2 _

'3/2.00

c) (5 pts) What will the voltage reading be when the external resistor is replaced by another one of700 Q?

- --

d) (4 pts) How much electrical energy is consumed on the R =700 Q resistor during 5 hrs?

10

phy142 exam1 fall11 solns

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