physics 1252 exam #4b (final) - physics and astronomy 1252 exam #4b (final) thu., 30 april 2015...

Physics 1252 Exam #4B (Final)Thu., 30 April 2015 Name:

Physics 1252Exam #4B (Final)

Instructions:This is a closed-book, closed-notes exam. You are allowed to use a clean print-out of yourformula sheet, any scientific calculator, and a ruler. Do not write on your formula sheet,except for your name: it must be handed in, signed but clean, with your exam.

There is space after each question to show your work; if you need more space, you may usethe back of the page, or request more paper. Please clearly indicate where your work foreach problem is. Underline or draw a box around your final answer.

The exam consists of four sections. Read all the questions at the start so that you canallocate your time wisely. Do easy ones first!

You may not share your calculator. The use of cell phones or any other electronic de-vices (besides calculators) is prohibited. All such gadgets must be turned off and put awaythroughout the exam.

• Do not open the exam until told to begin.

• You have the one entire class period to finish the exam.

• Put your last name on every page of the exam and on the formula sheet.

• You must provide explanations and/or show work legibly to receive full credit forSections II and III.

• Make sure that your answers include appropriate units and significant digits. (Note:For intermediate steps in your calculation, it’s best to carry more significant digits.)

• Fundamental constants and unit prefixes are on the Formula Sheet, last page.

By signing below, you indicate that you understand the instructions for this exam and agreeto abide by them. You also certify that you will personally uphold the university’s standardsof academic honesty for this exam, and will not tolerate any violations of these standards byothers. Unsigned exams will not be graded.

Signature:

UGACard #:

Copyright c© 2015 University of Georgia. Unauthorized duplication or distribution prohibited.


Section I II III IV V VI

Score /60 /35 /35 /35 /35 /10

I: Multiple-Choice Questions (60 points)

For each question below, choose the single best response and write the correspondingcapital letter in the box provided. There is no penalty for guessing the wrong answer.

1. A small particle of electric charge q is traveling in a uniform magnetic field, ~B. Which ofthe following figure panels could correctly represent the ~B-field direction; the magneticforce, ~F , exerted on the particle by the magnetic field; and either the particle’s velocityvector, ~v, or its q~v-vector, whichever is indicated in the panel.Fig. 3.55

(2)

B F

(3)

B

F

(4)

B

(1)

F

B B

(5)

F

F

qv qv

qv

v v

A. Panel (1), but only if q is negative.

B. Both Panels (2) and (3), but only if q is negative.

C. Panel (4), but only if q is positive.

D. Panel (5), regardless of the sign of q.

E. Panel (5), but only if q is positive.

2. A diffraction grating is illuminated with a laser beam at normal incidence. A 3rd orderprincipal intensity maximum is observed at an angle θ3 = 34.750o, measured fromthe central axis, and sin θ3 = 0.57. How many principal maxima, total, including thecentral maximum, can be observed across the entire, very wide (infinite-width) screen,i.e., between θ=−90o and θ=+90o?

A. 6B. 7C. 5D. 11E. 9

Copyright c© 2015 University of Georgia. 2


3. Visible light has a range of wavelengths from 400nm (violet) to 700nm (red) in vacuum.A beam of electromagnetic waves with a frequency of 714.3THz in air travels from airinto water, with indices of refraction nAir = 1.00 and nWater = 1.333. To an under-waterobserver, the beam while traveling in water will

A. have a wavelength of 559.9nm, have the same frequency as in air, and be visibleto the human eye;

B. have a wavelength of 315.1nm, have the same frequency as in air, and be invisibleto the human eye;

C. have a wavelength of 315.1nm, have the same frequency as in air, and be visibleto the human eye.

D. have a wavelength of 315.1nm, have a frequency of 952.2THz, and be invisibleto the human eye;

E. have a wavelength of 420.0nm, have a frequency of 535.9THz, and be visible tothe human eye;

4. In the figure below, Q1 and Q2 are negative point charges with |Q1| and |Q2| being ofcomparable magnitude. The point P and the locations of Q1 and Q2 form the threecorners of a square. Which arrow drawn at P could correctly represent the electricfield vector ~E generated by Q1 and Q2 at P ?

Q1

Fig. 2.30

Q2

P

(E) (D)

(C)

(B)

(A)

A. B. C. D. E.



5. Two large, metallic, planar, parallel, charged capacitor plates have an electric potentialdifference of ∆V = V2−V1 = 2500V, where V1 and V2 are the electric potentials on theleft and right plate, respectively, as shown here:

Fig. 2.32

Q2

Plate 2: Plate 1:

An electron is shot through a small hole in the left plate, into the space between thetwo plates. The electron, while traveling from the left to the right plate, ...

A. will lose 4.0 × 10−16J in kinetic energy between left and right plate, provided itreaches the right plate.

B. will gain 4.0× 10−16J in kinetic energy between left and right plate.C. must have a kinetic energy of at least 8.0 × 10−16J, as it passes through the left

plate, in order to reach the right plate.D. will gain 8.0× 10−16J in kinetic energy between left and right plate.E. will gain 2.0× 10−16J in kinetic energy between left and right plate.

6. In an electric generator, a single metallic wire loop, enclosing an area of 15cm2 andspinning in a uniform magnetic field ~B at 2100RPM, produces a maximum inducedelectromotoric force (EMF) of 5mV. What is the maximum induced EMF in a loop of

30cm2 area, spinning at 6300RPM in the same ~B-field?

A. 0.833mV

B. 30mV

C. 40mV

D. 3.75mV

E. 7.5mV



7. Two very long thin straight wires running parallel to the z-axis carry currents I1 (in−z-direction) and I2 (in +z-direction). The intersections of the wires with the x− y-plane and point P form 3 corners of a square, as shown here:

x

P

(E)(B)

(A)

(C)

Fig. 3.30

x-y-Plane Viewz

y

x

y(D)

I1I2

Which arrow drawn at point P in the x− y-plane could correctly represent the mag-netic field vector ~B produced by I1 and I2 at P?

A. B. C. D. E.

8. In the circuit fragment shown below, given currents are I1 = +8A and I3 = +2A; andresistances are Rb = 6 Ω and Rc = 10 Ω. What is the electrical potential differenceVbc ≡ Vb − Vc between points b and c in the circuit?

I1 Fig. 3.61

Rb

I3

I2

a

b

Rc c

Arrows indicate positive current directions: I>0 if |I| flowing into arrow direction I<0 if |I| flowing against arrow direction

A. +16VB. +40VC. +80VD. +56VE. −16V



II: Lateral and Angular Magnification by a Single Lens (35 points)

If a small object, 1.5mm in size, is placed 2.5cm from a lens the lens produces an erect,virtual image with a 5-fold lateral magnification.

(a) Find the image distance, d′, and, from that, the lens’s focal length, f . Is this aconvergent or a divergent lens?

(b) Find the angular magnification achieved with this placement of the object, comparedto viewing the same object from a near-point distance of 25cm without any opticalinstrument. Does the angular magnification depend on the size of the object?

(c) How far from this lens must the object be placed to produce an image with a lateralmagnification of −9. Is this a virtual or a real image? Is the image erect of inverted?



Work and Drawing Space for Problem II:



III: Electric Field from Point Charges (35 points)

A point charge of unknown amount, Q1, is positioned at an unknown location in the x-y-plane. It produces an electric field vector ~E1 ≡ [E1,x, E1,y, E1,z] with components E1,x =−2N/C, E1,y =+6N/C, E1,z =0, at an observation point, P ≡(xP , 0, 0) with xP =−4m, onthe x-axis.

A second point charge, Q2 = −80nC, is now added, placed at the origin, O, and both pointcharges combined, Q1 and Q2, then jointly produce a net electric field, ~E = [Ex, Ey, Ez].

(a) Calculate the components of ~E at P ; its strength, | ~E|; and its angle, θ, measured from

the +x-direction, with θ > 0 if ~E points above the x-axis, else θ < 0.

On the blank page attached, make a big drawing showing: x-axis; y-axis; O; P ; ~E1;the field contribution ~E2, produced by Q2 at P ; and ~E, as the resultant in a vectoraddition parallelogram, all field vectors with their tail ends attached to P .

(b) Now Q1 is removed and an electron is placed, at rest, at point P and then released,to accelerate subject to the electric field produced by Q2. Find the magnitude anddirection of the electron’s acceleration, ~a, immediately after its release at P .

Then also show ~a in the drawing from (a), correctly aligned with the relevant electricfield vector.

(c) In Part (b), what is the electron’s speed, if it travels infinitely far away from Q2?



Work and Drawing Space for Problem III:



IV: Circuit Analysis (35 points) In the circuit shown below, assume that I1 =9A,I4 = 5A, R2 = 7Ω, R3 = 4Ω, R4 = 8Ω, and C = 30 µF. Also assume that the capacitor isfully charged, by the voltage drop across it, and there is no current flowing to or from eithercapacitor plate.

R4 I4

R2 I2

E

Io

Fig. 3.49

I1 R1

R3 I3

x y RC C IC

a

b

p

q

(a) Find the total current, Io, flowing through the battery. Hints: Since there’s nocurrent to or from the capacitor plates, what is the current IC and/or the currentthrough RC? Use a junction (node) to find I2 or I3, then another junction to find Io.

(b) Find the battery voltage E . Hint: Use a junction to find I2, then a loop to find E .

(c) Find the total amount of electric field energy stored in the capacitor C. Hint: Usea loop to find Vy − Vx.



Work Space for Problem IV:



V: Flux and Induced Current in a Loop (35 points) The infinitely longstraight wire in the x-y-plane, shown below at d = 6cm from the x-axis, carries a time-dependent current, I(t), flowing in the −x-direction. I(t) increases linearly with time t at arate of ∆I/∆t= +0.5A/s, starting with I(0) = 0 at time t = 0. A narrow rectangular wireloop in the x-y-plane, with sidelengths a = 9cm and b = 0.3cm, is centered at the originO≡(0, 0, 0).

Fig. 4.15

x

y

z

y

x

I

Loop

a

b d

(a) Find the current I at time t1 = 6s, and the strength and direction of the magnetic field,~B, produced by that current at the center of the loop, O≡(0, 0, 0), at time t1 = 6s.

(b) Calculate the magnetic flux, Φm, through the loop time t1 = 6s, with the loop’s area

vector ~A defined to point in the +z-direction. Use the magnetic field vector, ~B, calcu-lated at the center of the loop and assume ~B is approximately uniform across the looparea. Also calculate the rate of change of this flux, ∆Φm/∆t.

(c) Find the current, IL, induced in the loop by the time-dependent flux, Φm, assumingthe loop wire has a resistance of 0.4Ω. Does IL flow clockwise or counter-clockwisearound the loop, as seen in the plane of the drawing above?



Work and Drawing Space for Problem V:



VI: Draw a Ray Diagram (Extra Credit: 10 points)

A virtual object is positioned to the left of a divergent lens, at a distance from the lenswhich is less than the absolute value of the lens’s focal length. Use a ruler to draw a cleanray diagram for the formation of the image, showing at least two of the principal rays, thelens and both its focal points, the object and the image, all of them clearly labeled. Alsoclearly label the incoming and the outgoing side of the lens. Is the image real or virtual?


physics 1252 exam #4b (final) - physics and astronomy 1252 exam #4b (final) thu., 30 april 2015...

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