Download exam i, physics 1306

FINAL EXAM, PHYSICS 2401, December 15, 2010, Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
1. PLEASE put your name on every sheet of paper you use and write on ONE SIDE of the
paper only!! PLEASE DO NOT write on the exam sheets, there will not be room!
2. PLEASE show all work, writing the essential steps in the problem solution. Write
appropriate formulas first, then put in numbers. Partial credit will be LIBERAL, provided
that essential work is shown. Organized, logical, easy to follow work will receive more credit
than disorganized work.
3. The setup (PHYSICS) of a problem will count more heavily than the math of working it out.
4. PLEASE write neatly. Before handing in solutions, PLEASE: a) number the pages & put the
pages in numerical order, b) put the problem solutions in numerical order, & c) clearly mark
your final answers. If I can’t read or find your answer, you can't expect me to give it the
credit it deserves.
5. NOTE!! The words “EXPLAIN”, “DISCUSS” & “DEFINE” below mean to answer mostly
in ENGLISH, NOT math symbols!
PLEASE HELP ME GRADE EFFICIENTLY BY FOLLOWING
THESE SIMPLE INSTRUCTIONS!!! FAILURE TO FOLLOW
THEM MAY RESULT IN A LOWER GRADE!! THANK YOU!!
Two 8.5’’ x 11’’ pieces of paper with anything on them & a calculator are allowed. The following is
DIFFERENT for this Exam!! Questions 1 AND 2 (Conceptual) are REQUIRED! NOTE: You
MUST ALSO WORK Problem 3 OR Problem 4 (Magnetism)!! Also work any two (2) of the
remaining problems for five (5) problems total on the exam. Each problem is equally weighted & worth 20
points, for a total of 100 points. Answer all parts of the ones you choose!
NOTE ON MANDATORY CONCEPTUAL QUESTIONS #1 & #2!!! Answer briefly all parts of
both questions in a few complete, grammatically correct English sentences. I want answers which use
mainly ENGLISH WORDS, NOT symbols or equations! If you insist on using symbols, DEFINE all
symbols you use! (Note: Answers with ONLY symbols, with no WORD explanations get ZERO credit!).
1. MANDATORY CONCEPTUAL QUESTIONS on Chs. 21-28 & 32-35.
a. State Snell’s Law of Refraction.
b. State Huygens’ Principle for light waves.
c. State Coulomb’s Law.
(a)
(b)
Fig. 1
d. State Gauss’s Law.
e. State Ampère’s Law.
f. State the Biot-Savart Law.
g. Figure 1 shows 4 long parallel wires which carry equal currents into or out of the page. In which
configuration, (a) or (b), is the magnetic field greater at the center of the square? Explain WHY
you answered the way you did!
h. Briefly Define the following terms: i) Electric Field, ii) Electric Flux, iii) Electric Potential,
iv) Magnetic Field, v) Magnetic Flux.
2. MANDATORY CONCEPTUAL QUESTIONS on Ch. 29 & Ch. 31.
a.
b.
c.
d.
e.
State Faraday’s Law of Induction.
State Lenz’s Law.
State Gauss’s Law for Magnetism. The physical (& philosophical) interpretation of this Law
was discussed in class (& is also in Ch. 31). Briefly summarize this interpretation.
Briefly Define the following terms: i) Electromotive Force (emf), ii) Displacement Current,
iii) Electromagnetic Wave.
In class, we discussed the fact that, to arrive at the relations known as Maxwell’s Equations,
Maxwell made a modification to Ampère’s Law so that it’s form resembled (but wasn’t exactly
the same as!) Faraday’s Law with the electric field E & the magnetic field B interchanged & the
electric flux ΦE & the magnetic flux ΦB interchanged. This is discussed in in Ch. 31. Briefly tell
me what modification Maxwell made to Ampère’s Law to achieve this result.
NOTE: QUESTION 2 CONTINUES ON THE NEXT PAGE!!
QUESTION 2, CONTINUED!!
f.
g.
h.
State Maxwell’s Equations of Electromagnetism.
As discussed in class & in Ch. 31, each of Maxwell’s Equations is a Law that was discussed by
itself in earlier chapters & each goes by its own name. Tell me the name of the Law that is
represented by each of Maxwell’s Equations.
5 POINT BONUS!! When Maxwell’s Equations are combined to show that Electromagnetic
Waves are produced by time varying fields, it is found that, in vacuum, the velocity of these
waves c is exactly the speed of light in vacuum. In this derivation, it is shown that c can be
expressed in terms of two fundamental constants that are used in earlier chapters: The
permittivity of free space: ε0 = 8.85  10-12 C2/(N m2) & the permeability of free space:
μ0 = 4π  10-7 T m/A. Write the equation which relates c to ε0 & μ0.
NOTE: WORK EITHER PROBLEM 3. OR PROBLEM 4. (Magnetism)!!!!!
3. Figure 2 shows two parallel segments of long straight wire of length
↑
ℓ = 2.0 m, a distance d = 10 cm apart, carrying currents I1 = 7.0 A &
↑ ← d → Fig. 2
I2 = 9.0 A in opposite directions. Figure 3 shows a cross section of
these wires in a plane perpendicular to the wires in Fig 2. Calculate:
ℓ
a. The magnitude and direction of the magnetic field B1 due to
current I1 at distance r = (½)d halfway between the two wires.
↓
State the direction of B1 by describing the way it points in Fig. 3.
b. The magnitude and direction of the magnetic field B2 due to
↓
current I2 at distance r = (½)d halfway between the two wires.
State the direction of B2 by describing the way it points in Fig. 3.
c. The magnitude and direction of the total magnetic field B at
←d→
Fig. 3
I1 (out)
I2 (in)
distance r = (½)d halfway between the two wires.
d. The magnitude and direction of the magnetic force F between the
two wires. State the direction of F by describing the way it points in Fig. 3.
Answer parts e & f briefly using correct English, NOT with symbols!
e. What Physical Principle did you use to calculate the magnetic fields in parts a & b?
f. 5 POINT BONUS!! The force in part d is calculated by using the expression for the
magnetic force on a current carrying wire in an external magnetic field. The force
calculated using that expression with field B1 & current I2 is the same as that calculated
using that expression with field B2 & current I1. What Physical Principle (from Physics
I!) requires that the previous statement is true?
NOTE: WORK EITHER PROBLEM 3. OR PROBLEM 4. (Magnetism)!!!!!
4. Figure 4 shows a long, straight, cylindrical wire conductor of
radius R, carrying a current I of uniform density in the
conductor. For the following, assume that r, the radial distance
from the axis, is much less than the length of the wire.
Calculate the magnetic field B due to this current:
a. At all points outside the conductor (r > R).
b. At all points inside the conductor (r < R).
Fig. 4
Answer part c briefly using correct English, NOT with
symbols!
c. What Physical Principle did you use to calculate the
magnetic fields in parts a & b?
For R = 3.0 mm and I = 65 A, Calculate B:
d. At r = 1.5 mm.
e. At r = 3.0 mm.
f. At r = 4.5 mm.
NOTE: WORK ANY TWO (2) OF PROBLEMS 5., 6., & 7!!!!!
5. Figure 5 shows a non-conducting sphere of radius r0, which contains a spherical cavity of
radius r1 (r1 < r0) centered at the same point as the larger sphere. A
Fig. 5
positive charge Q is uniformly distributed throughout the volume
between the spheres (between r1 & r0).
Calculate:
a. The electric field outside the outer sphere (r > r0).
b. The electric field inside the inner sphere (0 < r < r1).
c. The electric field between the inner & outer spheres (r1 < r < r0).
d. The electric potential outside the outer sphere. (r > r0)
e. The electric potential inside the inner sphere (0 < r < r1).
f. The electric potential between the inner & outer spheres (r1 < r < r0).
The following may be needed: Differential volume element in spherical coordinates (with no
angular dependence): dV = 4πr2dr. Integral of r to a power ∫rndr = [rn+1/(n+1)] (n ≠ -1).
NOTE: WORK ANY TWO (2) OF PROBLEMS 5., 6., & 7!!!!!
6. See Figure 6. A light beam in air strikes a 4.0 cm thick piece of plastic (refractive index n1 =
1.75) at an angle θ1 = 45° as shown. The plastic is on top of a
6.0 cm thick piece of glass (refractive index n2 =
air
1.54). The speed of light in vacuum is c = 3.0  108
4.0 cm 
n1 = 1.75
m/s. The index of refraction of air is n = 1.00.

Calculate:
a. The angle θ2 shown in the figure.
b. The speed of light v1 in the upper plastic layer.
c. The angle θ3 shown in the figure.
d. The speed of light v2 in the lower glass layer.
e. The angle θ4 shown in the figure.
f. The distance D shown in the figure.
7.
6.0 cm
θ2


NOTE: WORK ANY TWO (2) OF PROBLEMS 5., 6., & 7!!!!!
Answer parts a & b briefly using correct English, NOT with symbols!
a. State Kirchhoff’s Junction Rule for electrical circuits.
What Physical Principle is the basis for this Rule?
b. State Kirchhoff’s Loop Rule for electrical circuits.
What Physical Principle is the basis for this Rule?
For the electrical circuit in Fig. 7, Calculate (in any order!)
c. The current I1.
d. The current I2.
e. The current I3.
f. The power dissipated in the 30 Ω resistor.
n2 = 1.54
θ3
θ4
Fig. 6
Fig. 7