Download 95.144 Final Exam Spring 2015

 1
95.144 Final Exam Spring 2015
Section instructor____________________
Section number__________
Last/First name__________________________________________________________
Last 3 Digits of Student ID Number: __________
Show all work. Show all formulas used for each problem prior to substitution of
numbers.
Label diagrams and include appropriate units for your answers.
You may use an alphanumeric calculator during the exam as long as you do not program
any formulas into memory. By using an alphanumeric calculator you agree to allow us
to check its memory during the exam. Simple scientific calculators are always OK!
A Formula Sheet Is Attached To The Back Of This Examination
Be Prepared to Show your Student ID Card
Score on each problem:
1. (30)
____
2. (20)
____
3. (20)
____
4. (20) ____
5. (20) ____
6. (20) ____
7. (20) ____
Total Score (out of 150 pts)
____
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1. Conceptual Questions (30 point)
1.1. (6pts) A lens produces a sharply focused, inverted image on a screen. What will
you see on the screen if a piece of dark paper is lowered to cover the top half of the
lens?
A. An inverted but blurry image.
B. An image that is dimmer but
otherwise unchanged.
C. Only the top half of the image.
D. Only the bottom half of the image.
E. No image at all.
1.2. (6pts) The photograph shows a reflection in the bowl of
spoon. Is this image created by
A) a concave surface of the spoon?
B) a convex surface of the spoon?
1.3 (6pts) A negatively charged particle moves along a
very long wire with a current as it is shown in the figure.
What is the direction of the force acting on the particle?
A) there is no force
B) to the left
C) to the right
D) into the page
E) out of the page
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1.4 (6pts) An extended light bulb (see
the figure) illuminates a narrow vertical
aperture in a dark screen. What do you
see on the viewing screen?
(Circle the right answer)
1.5 (6pts) A parallel-plate capacitor initially has a potential difference of 400 V
and is then disconnected from the charging battery. If the plate spacing is now
doubled, what is the new value of the voltage?
A) 100 V
B) 200 V
C) 400 V
D) 800 V
E) 1600 V
Problem 2. (20 pts)
A 0.1-m-tall cat is placed 20 cm from a 1-m-focal length converging lens.
a) Determine the image position using ray tracing (draw it). Identify if the image
is upright/inverted and real/virtual.
b) Calculate the image position and height.
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Problem 3. (20 pts)
The block of glass shown in cross section in the figure is surrounded by air. A ray of
light enters the block at its left-hand face with incident angle θ1 and reemerges into the
air from the right-hand face directed parallel to the block’s base. Determine θ1.
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Problem 4. (20 pts)
Monochromatic light falls on two very narrow slits 0.048 mm apart. Successive fringes
on a screen 6.00 m away are 8.5 cm apart near the center of the pattern. Determine the
wavelength and frequency of the light.
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Problem 5. (20 pts)
The electric field of an electromagnetic wave in a vacuum is
.
.
∙
;
;
,
where x is in meters and t is in seconds. What are the wave’s
a) direction of propagation;
b) wavenumber;
c) wavelength;
d) frequency;
e) magnetic field amplitude?
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Problem 6. (20 pts)
A circular loop 10 cm in radius with a resistance of 0.4 Ω is in a magnetic field of 0.6 T
whose direction is perpendicular to the plane of the loop. The loop is grasped at
opposite ends of a diameter and pulled out into a rectangle 30 cm long and 1.4 cm wide
in a time of 0.2 seconds.
a)
b)
c)
d)
Find the magnetic flux through the circular loop;
Find the magnetic flux through the rectangular loop;
Find the average EMF in the wire while it is being deformed
Find the average current in the wire while it is being deformed.
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Problem 7. (20 pts)
The electric field strength is 50,000 N/C inside a parallel plate capacitor with a 2.0 mm
spacing. A proton is released from rest at the positive plate. What is the proton’s speed
when it reaches the negative plate?
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Formula Sheet:
Electricity and Magnetism
Potential Energy
Coulomb’s law
Two point charges Electric Field
Capacitors
Δ
Parallel-plate
Field of a point charge Electric field inside a capacitor
Capacitors connected in parallel
⋯
Capacitors connected in series
1
1
1
⋯
Energy stored in a capacitor
Principle of superposition
Ohm’s law
Electric flux
∙
Φ
Gauss’s law
Φ
∙
Δ
Electric potential
0
Power
Resistors connected in series
ΔV
For a point charge For a paralle-plate capacitor
∙
⋯
Resistors connected in parallel
1
1
1
1
⋯
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The potential difference across a
charging capacitor in RC circuit
Maxwell’s equations
∙
1
A magnetic field exerts a force
∙
Ɛ
0
Φ
∙
Φ
∙
The Biot-Savart Law
̂
4
̂
4
The magnetic field of:
A straight line wire
The Poynting vector
1
Malus’s Law
2
A solenoid
Traveling Wave
,
Magnetic flux
Φ
2
∙
Inductance
2
;
Interference
Φ
Δ
2
Δ
Δ
μ
Δ
Energy stored in an inductor
2
2 Δ
Δ
1
2 2
2acos
“Discharged” LR circuit
;
;
/
Δ
2
12
Standing Waves
A(x)=2aSin(kx)
2
;
2
Double Slit
Diffraction grating
Constants
Charge on electron
1.60 ∙ 10 Electron mass
9.11 ∙ 10 Proton mass
1.67 ∙ 10 Permittivity of free space
8.85 ∙ 10 /
Permeability of free space
4 ∙ 10 /
1
sin
4
tan
Thin-lens equation:
1
1
1
; | |
Snell’s Law:
sin
TIR:sin
sin
8.99 ∙ 109 3.0 ∙ 10
2
/
2
/
Kinematic eq-ns with const. Acc.:
v(t) = v0x+at
x(t) = x0+ v0xt +(1/2) at2
v2 = v0x2 + 2a(x – x0)
Centripetal acceleration
L=2πR
A=πR2
V=(4/3)πR3
⁄