Midterm 4 Statistics
Bin
count
average
median
st dev
hi
lo
0
5
10
15
20
25
30
35
40
45
50
55
60
Frequency
0
1
1
7
15
12
30
44
52
61
40
26
4
60 pts
293
37
39
10.37904
58
3
100%
293
62.21133
65.00001
17.2984
95.83335
5.000001
70
60
50
40
30
20
10
0
0
5
Physics 2220 - Fall 2016 - Exam 4
Average=37 pts (62%)
10 15 20 25 30 35 40 45 50 55 60
FINAL REVIEW
Review F1
A spherical non-conductor has a uniform volume charge density
ρ and radius R. Given: R, ρ use Gauss’ law to find:
(a) The electric field at a distance r > R
(b) The electric field at a distance r < R
(c) The potential difference between two points at distances
y
rB > R and rA < R.
qin = rVin
R
x
You need to split the
integral into two parts
Review F2
A uniformly charged rod of length L and charge Q has the
shape of a semicircle.
(a) Calculate the Electric field at the center of the circle P.
(b) Find the work needed to bring a charge q from ∞ to P.

dq
E  ke  2 rˆ
r
Only the y component is not
zero. The x component is
zero because of symmetry
Q
dq = l ds = ds
L
VP = ke ò
dq
r
ds  Rd
V¥ = 0
DU = qDV
Review F3
The switch S is closed for a long time and charges the
capacitors. There is a dielectric κ in C3. (All capacitor values
are given without dielectric).
Find the charge and potential on each capacitor.
S
Q
Cº
V
ε
C   C0
C1
C2
Qtotal = Ctotale
Ctotal = (1/ C1 +1/ (C2 + k C3 ))-1
Q1 = Qtotal
Q2 + Q3 = Qtotal
V2 = V3
C3
κ
Review F4
The switch is closed at t = 0.
(a) Find the voltage across each resistor at t = 0.
(b) Find the voltage across each resistor at t = ∞.
(c) The capacitor is fully
charged and the switch is
opened. Calculate the
time constant for
discharging the capacitor.
(d) Find the charge on
the capacitor, Q(t), after
the switch is opened.
S
R1
C
ε
R2
R3
Review F4 solution
The switch is closed at t = 0.
(a) At t = 0 the capacitor is like a wire. Redraw the circuit and
find the currents.
(b) At t = ∞ there is no current in R2. Redraw the circuit and
find the currents.
(c) Redraw the circuit
without the battery and R1.
S
R1
t = (R2 + R3 )C
(d) Find the charge on the
capacitor, Q(t), after the
switch is opened.
Q(t) = Qmax e-t/t
C
ε
R2
R3
Review F5
(a) Find the equivalent resistance of the circuit. R eq =15W
(b) Find the current through the battery. I bat = I1 =15.0V / R eq
(c) Find the potential difference across ac.
Vac = R1I1
(d) Write Kirchhoff’s rules for the circuit.
Review F6
A long coaxial cable has current +I
on the interior cable and -I on the
exterior cable. The current density
J is uniform over the cross section
of the interior conductor.
(a) Calculate the magnetic field at
r < a, a < r < b and r > b.
(b) Calculate the magnetic energy
stored between the cables in
one meter of the coaxial cable.
dI I
J=
=
dA A
uB =dU/dV=B2/2μ0
U = ò uB (r) dV
dV = 2p rldr
b
U = 2p l ò uB (r)rdr
a
Review F7
Three very long straight wires carrying currents I1 = -10.0 A
(into the paper) and I2 = 5.00 and I3 = 8.00 A are
perpendicular to the paper. The side a is 10.0 cm.
(a) Find the total magnetic field, magnitude and direction, at
point P.
(b) Find the total force per meter, magnitude and direction, on
I3 exerted by the other two currents.
m0 I
B(r) =
2p r
.P
a
Use right hand rule to find
the directions and find BP,x
I1
and BP,y components.
a
I2
m0 I1I 3
F13 =
l
4p a
m0 I 2 I3
F23 =
l
2p a
I3
Review F8
Two very long wires are parallel and a distance d apart. The
wires carry a current I in opposite directions and its magnitude is
given by I = I0 e-ωt. Given: I0, d and ω.
(a) Find the magnetic field
generated by the two wires as a
function of time at a point P located
between the wires, at a distance r
from the left wire.
(b) Calculate the magnetic flux
through the rectangular wire loop
shown as a function of time. (the
dimensions l and a are given)
(c) Calculate the induced emf in
the loop as a function of time.
d
r
-I
.P
a
a
l
I
Review F8 solution
Two very long wires are parallel and a distance d apart. The
wires carry a current I in opposite directions and its magnitude is
given by I = I0 e-ωt. Given: I0, d and ω.
d
m0 I
m0 I
B(r) =
+
2p r 2p r(d - r)
r
-I
eind
dFB
=dt
.P
a
a
l
I
Review F9
A circular wire loop of radius r and resistance R turns about a
vertical axis with constant angular speed ω in a region of
constant uniform magnetic field B perpendicular to the
rotation axis. At t = 0 the unit vector normal to the loop is in
the direction of B.
(a) Find the magnetic flux
through the loop as a function
of time.
(b) Find the induced current in
the loop as a function of time.
(c) What is the net magnetic
force on the loop?
Review F9 solution
A circular wire loop of radius r and resistance R turns about a
vertical axis with constant angular speed ω in a region of
constant uniform magnetic field B perpendicular to the
rotation axis. At t = 0 the unit vector normal to the loop is in
the direction of B.
dFB
e =dt
I =e / R
Review F10
The switch is connected to position a for a long time. At t = 0
the switch is thrown to position b. After this time find:
(a) The frequency of the LC circuit.
(b) The charge on the capacitor and the current and the
voltage in the inductor as functions of time.
w= 1
(c) The total energy of the circuit at t = 3.00 s.
LC
Qmax = eC
Q(t) = Qmax cos(w t)
I(t) =
dQ
dI
, VL (t) = -L
dt
dt
1
Utot (t) = Ce 2 = constant
2