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Unformatted text preview: PHYS 2212 Test 2
Spring 2011
Name(print)
Instructions
• Read all problems carefully before attempting to solve them.
• Your work must be legible, and the organization must be clear.
• You must show all work, including correct vector notation.
• Correct answers without adequate explanation will be counted wrong.
• Incorrect work or explanations mixed in with correct work will be counted wrong. Cross out anything
you don’t want us to read!
• Make explanations correct but brief. You do not need to write a lot of prose.
• Include diagrams!
• Show what goes into a calculation, not just the ﬁnal number, e.g.:
5 × 104 a·b
c·d = (8×10−3 )(5×106 )
(2×10−5 )(4×104 ) = • Give standard SI units with your results.
Unless speciﬁcally asked to derive a result, you may start from the formulas given on the
formula sheet, including equations corresponding to the fundamental concepts. If a formula
you need is not given, you must derive it.
If you cannot do some portion of a problem, invent a symbol for the quantity you can’t
calculate (explain that you are doing this), and use it to do the rest of the problem. Honor Pledge
“In accordance with the Georgia Tech Honor Code, I have neither given
nor received unauthorized aid on this test.” Sign your name on the line above PHYS 2212
Do not write on this page!
Problem
Problem
Problem
Problem
Problem Score
1
2
3
4 (25
(25
(25
(25 pts)
pts)
pts)
pts) Grader Problem 1 (25 Points) Consider a very thin glass rod bent
into a halfcircular arc that has uniform charge Q and radius R. Answer
the following questions to determine
the electric ﬁeld at a point on the
zaxis.
(a 5pts) Consider an inﬁnitesimal slice of the bent rod with angular
length dθ located at an angle θ from
the right end of the rod as indicated
in the ﬁgure.
Find the position
vector r that points from center of
this slice to the observation location
A =< 0, 0, L > on the zaxis. (b 5pts) Determine an expression for the charge of the slice, dQ, in terms of the inﬁnitesimal angular length
dθ and relevant known variables. (c 10pts) Derive an expression for the vector electric ﬁeld dE of the slice of the rod at the observation
location A in terms of the given variables and known constants. (d 5pts) Integrate over the charge distribution to determine the electric ﬁeld E at observation location A.
You answer should only contain the given variables and known constants. Problem 2 (25 Points) An isolated largeplate capacitor (not
connected to anything) originally has
a potential diﬀerence of 500 volts with
an air gap of 6 mm. Then a plastic
slab 2 mm thick, with dielectric
constant 4, is inserted into the air gap
as shown in the diagram.
(a 2pts) Draw the orientation of
the induced dipoles in the plastic
slab.
(b 5pts) Draw three arrows representing the net electric ﬁeld in the
three regions inside the capacitor.
Recall that longer arrows mean larger
magnitudes. For the plastic slab,
draw the average electric ﬁeld. (c 5pts) Determine the potential diﬀerence V1 − V2 . Be sure to show all of your work (d 5pts) Determine the potential diﬀerence V2 − V3 . Be sure to show all of your work (e 5pts) Determine the potential diﬀerence V3 − V4 . Be sure to show all of your work (f 3pts) Determine the potential diﬀerence V4 − V1 . Be sure to show all of your work Problem 3 (25 Points) A thin spherical shell made of
plastic carries a uniformly distributed negative charge −Q1 .
Two large thin disks made of glass
carry uniformly distributed positive and negative charges +Q2 and
−Q2 . The radius of the plastic
spherical shell is R1 and the radius of the glass disks is R2 . Note
that the diagram is not drawn to
scale and R1 << R2 (i. e. the disks
make up a capacitor). Calculate
the potential diﬀerence V3 − V2 . Problem 4 (25 Points) N
y A straight wire 15 m long (the rest of
the circuit is not shown here) oriented
along the y axis, lies below a compass
as shown. The wire is much longer
than is shown here and the diagram is
not to scale. The compass is centered
on the origin and is 4 mm above the
wire. When a conventional current of
I amperes ﬂows through the wire, the
compass deﬂects 8◦ to the west. x (a 5pts) On the diagram draw the direction of the conventional current I in the wire. Brieﬂy explain how
you determined this. (b 15pts) Determine the magnitude of the conventional current I ﬂowing through the wire and be sure to
show all of your work. (c 5pts) With the current still running in the straight wire, a current carrying loop is placed near the
compass, and the compass now deﬂects 16◦ to the west. Which of the diagrams below indicates where the
loop was placed? The directions indicated in the diagrams below refer to the conventional current. Circle
the diagram of your choice . Your answer must be consistent with part (a).
N
N (a) (b) y y conventional current flows
clockwise, viewed from
top of ring conventional current flows
clockwise, viewed from
top of ring
x (c) x (d) y y
N N x conventional current flows
clockwise, viewed from
right of ring x conventional current flows
counterclockwise, viewed
from right of ring This page is for extra work, if needed. Things you must know
Relationship between electric ﬁeld and electric force
Electric ﬁeld of a point charge
Relationship between magnetic ﬁeld and magnetic force
Magnetic ﬁeld of a moving point charge Conservation of charge
The Superposition Principle Other Fundamental Concepts
dp
dp
= Fnet
and
≈ ma if v << c
dt
dt
f
∆V = − i E • dl ≈ − (Ex ∆x + Ey ∆y + Ez ∆z )
Φmag = B • ndA
ˆ dv
dt
∆Uel = q ∆V
Φel = E • ndA
ˆ
qinside
E • ndA =
ˆ a= 0 emf = EN C • dl = B • ndA = 0
ˆ
dΦmag
dt Iinside path + B • dl = µ0 B • dl = µ0
0 d
dt Iinside path E • ndA
ˆ Speciﬁc Results
1 2qs
(on axis, r
s)
4π 0 r 3
Q
1
(r ⊥ from center)
Erod =
4π 0 r r 2 + (L/2)2
1 2Q/L
Erod ≈
(if r
L)
4π 0 r
z
Q/A
(z along axis)
1− 2
Edisk =
20
(z + R2 )1/2
Q/A
(+Q and −Q disks)
Ecapacitor ≈
Edipole,axis ≈ 0 µ0 I ∆ × r
ˆ
∆B =
(short wire)
2
4π
r
µ0
µ0 2I
LI
Bwire =
≈
(r
2 + (L/2)2
4π r r
4π r 1 −qa⊥
4π 0 c2 r
i = nAv
¯ Erad = σ = q  nu
Edielectric = Eapplied
K 1 qs
(on ⊥ axis, r
4π 0 r 3 s) electric dipole moment p = qs, p = α Eapplied
qz
1
(z along axis)
2 + R2 )3/2
4π 0 (z
Q/A
Q/A
z
Edisk ≈
≈
(if z
R)
1−
20
R
20
Q/A s
just outside capacitor
Ef ringe ≈
2R
0
Ering = ∆F = I ∆l × B
L) µ0 2IπR2
2IπR2
µ0
≈
(on axis, z
4π (z 2 + R2 )3/2
4π z 3
µ0 2µ
Bdipole,axis ≈
(on axis, r
s)
4π r 3
Bloop = Edipole,⊥ ≈ Bwire = Bearth tan θ
R) µ = IA = IπR2 Bdipole,⊥ ≈ µ0 µ
(on ⊥ axis, r
4π r 3 ˆ
ˆ
v = Erad × Brad
ˆ Brad = I = q  nAv
¯
I
J=
= σE
A
1
q
1
∆V =
−
4π 0 rf
ri v = uE
¯
L
R=
σA
due to a point charge s) Erad
c I=  ∆V 
for an ohmic resistor (R independent of ∆V );
R Q = C ∆V  power = I ∆V Power = I ∆V K ≈ 1 mv 2 if v
2 c I= circular motion: dp
v 
mv 2
=
p ≈
dt ⊥
R
R ∆V 
(ohmic resistor)
R Math Help a × b = ax , ay , az × bx , by , bz
= (ay bz − az by )ˆ − (ax bz − az bx )ˆ + (ax by − ay bx )ˆ
x
y
z dx
= ln (a + x) + c
x+a dx
1
=−
+c
2
(x + a)
a+x a dx = ax + c
Constant
Speed of light
Gravitational constant
Approx. grav ﬁeld near Earth’s surface
Electron mass
Proton mass
Neutron mass
Electric constant
Epsilonzero
Magnetic constant
Muzero
Proton charge
Electron volt
Avogadro’s number
Atomic radius
Proton radius
E to ionize air
BEarth (horizontal component) ax dx =
Symbol
c
G
g
me
mp
mn
1
4π 0
0 µ0
4π
µ0
e
1 eV
NA
Ra
Rp
Eionize
BEarth a2
x +c
2 dx
1
=−
+c
3
(a + x)
2(a + x)2
ax2 dx = a3
x +c
3 Approximate Value
3 × 108 m/s
6.7 × 10−11 N · m2 /kg2
9.8 N/kg
9 × 10−31 kg
1.7 × 10−27 kg
1.7 × 10−27 kg
9 × 109 N · m2 /C2
8.85 × 10−12 (N · m2 /C2 )−1
1 × 10−7 T · m/A
4π × 10−7 T · m/A
1.6 × 10−19 C
1.6 × 10−19 J
6.02 × 1023 molecules/mole
≈ 1 × 10−10 m
≈ 1 × 10−15 m
≈ 3 × 106 V/m
≈ 2 × 10−5 T ...
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This note was uploaded on 05/23/2011 for the course PHYISCS 2212 taught by Professor Shatz during the Spring '10 term at Georgia Institute of Technology.
 Spring '10
 SHATZ

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