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UCSD Physics 2B
Summer Session 2
SAMPLE Final Exam
HOW TO PREPARE FOR THIS EXAM
Make your formula sheets early so you can a ) Use them while working this Sample Exam
b ) Make sure you have everything you'll need
You may bring FIVE double-sided sheets to the final
However, this is not enough room to include everything!
Purge redundant formulas and include only what you really need.
It is extremely important to understand what the formulas mean and
how they are used. You may want to include notes on properties of
e.g., conductors and capacitors and inductors as circuit elements.
For example, look at problem # 11 in Part 2
You can work your problems out on scratch paper
BUT make sure to re-write them clearly on this exam
in brief yet complete form so we can follow your thinking.
Remember that you MUST show your work to receive credit
PART 1
1.
Multiple Choice
Coulomb Force
A positive charge of 45.0 nC is 25.0 mm from a negative charge of 63.0 nC. The force on one charge
due to the other is approximately
A. 2.26 × 10 −3 N
B. 1.13 × 10 −7 N
C. 4.08 × 10 −2 N
D. 1.13 × 10−13 N
E.
4.08 × 10 −4 N
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2.
Charge
How many electrons must be transferred to a body to produce a charge of 410 nC?
A. 1.25 × 10 −7
B. 1.60 × 10 −19
C. 1.28 × 10 +12
D. 3.45 × 10 +11
E. 2.56 × 10 +12
3.
Electric Field
A charge q = 23 mC feels a force of 1200 N at a certain point in space. What is the magnitude of the
electric field at that point?
A. 2.0 × 10 +4
N
C
B. 5.2 × 10 +4
N
C
C. 2.0 × 10 +7
N
C
D. 1.9 × 10 −5
N
C
E.
4.
None of these
Potential
The potential at a point due to a positive charge is found to be V. If the distance between the charge
and the point is reduced to half it's original distance, the potential becomes
A.
B.
C.
D.
E.
2V
V/2
V/4
4V
16 V
2
5.
Capacitance
The equivalent capacitance of two capacitors in parallel is
A.
B.
C.
D.
E.
6.
the sum of the their capacitances
the sum of the reciprocals of their capacitances
the reciprocal of the sum of the reciprocals of their capacitances
always less than the smallest of their capacitances
described by none of the above
Resistance
The equivalent resistance of two identical resistors in parallel is
A.
B.
C.
D.
E.
7.
twice the resistance of each one
half the resistance of each one
the reciprocal the resistance of each one
the square root of the resistance of each one
described by none of the above
Current
If 475 x 1016 electrons pass a particular point in a wire every minute, what is the current in the wire?
A.
B.
C.
D.
E.
760 mA
45.6 A
12.7 mA
79.0 A
1.32 A
3
8.
Current Density
A wire of radius 3.6 cm is carrying a current of 12 A. What is the current density J in the wire?
A. 3.9 A/m23.9
A
m2
kA
m2
A
C. 2.9 × 10 2 2
m
mA
D. 340 2
m
MA
E. 1.2 2
m
B. 4.4 × 10 2
9.
Ohm's Law
A heating coil operates at 210 V. If it draws 10.5 Amps, find its resistance.
A.
B.
C.
D.
E.
10.
11.1 Ω
20.0 Ω
50.0 mΩ
128 Ω
None of these
Power & Energy
How much electric energy (in Joules) is delivered in 90 seconds to an automobile electric starter
motor that draws 52.0 Amps from a 12.0 Volt battery?
A.
B.
C.
D.
E.
56.2 kJ
3.60 kJ
180 J
390 J
0.093 mJ
4
11.
Magnetic Field
What must be the current through a circular loop with a diameter of 17.0 mm for it to have
a magnetic field at its center of 3.28 x 10-4 T?
A.
B.
C.
D.
E.
12.
226 mA
45.2 mA
8.85 A
4.43 A
2.21 A
Faraday's Law
How much does the maximum emf produced by a generator (a rotating coil) change if the period of
rotation is doubled?
A.
B.
C.
D.
E.
13.
It is the same
It is doubled
It is quadrupled
It is halved
It is quartered
AC Circuits
The rms value of house voltage on Mars should be 440 V. What is the peak voltage?
A.
B.
C.
D.
E.
440 V
622 V
311 V
220 V
110 V
5
14.
AC Circuits
The generators at a power plant operate at 2500 V. If the primary of the transformer has 300
windings, and the secondary has 18,000 windings, what is the transmission voltage?
A.
B.
C.
D.
E.
15.
563 V
150,000 V
241,000 V
1440 V
none of these
LC Circuits
In the circuit below, C = 0.260 mF and L = 0.370 mH. What is the natural oscillation frequency of
the circuit?
A.
B.
C.
D.
E.
3.10 x 10-4 rad/sec
1.04 x 10 7 rad/sec
9.65 x 10-8 rad/sec
3.22 x 10 3 rad/sec
none of these
6
16.
RC Circuit
In the circuit shown below, C = 55 mF and R = 160 Ohms. What is the time constant of the circuit?
A.
B.
C.
D.
E.
17.
8.80 s
114 ms
2910 s
344 ms
zero
Inductance
A coil with a self-inductance of 6.5 H carries a current that is changing at the rate of 50 A/s. What is
the induced emf across the coil?
A.
B.
C.
D.
E.
18.
0.13 V
7.7 V
32 V
65 V
0.33 kV
Units
The Volt is a unit of
A.
B.
C.
D.
E.
capacitance
charge
energy
momentum
potential
7
19.
Units
The Farad is a unit of
A.
B.
C.
D.
E.
capacitance
charge
energy
momentum
potential
8
Part 2
Numeric Response
You must show your work to receive full credit.
Please box your final answers.
1.
Capacitance
A 3.0 μ F capacitor has a potential difference of 5000 V. How much work was done in charging it?
Answer ________________
2.
Capacitor Network
The circuit has been ‘on’ for a long time and all the capacitors are fully charged. The potential
along the bottom wire is defined to be zero. What is the voltage Vb at the point labeled ‘b’?
Answer _________________________
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3.
Electric Dipole
An electric dipole p of magnitude 25 nC·m makes an angle of 65º with a uniform electric field E of
magnitude 3.0 x 10-6 N/C. What is the magnitude of the torque on the dipole?
Answer __________________
4.
Potential
A uniform electric field exists between two parallel plates separated by 2.4 cm. The intensity of the
field is 23 kN/C. What is the potential difference between the plates?
Answer __________________
5.
Potential
Two concentric spheres carry opposite charges as shown below. What is the magnitude of the
electric potential difference between them?
Answer _____________________
10
6.
Resistor Circuit
Find the power dissipated by in the circuit shown below if V = 50.0 V, R1 = 25.0 Ω and R2 = 17.2
Ω.
Answer __________________
7.
Resistor Circuit
Find the potential difference between point A & B in the circuit diagram below. The resistances are
all in Ohms. Hint: turn this circuit into two parallel voltage dividers.
Answer __________________
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8.
Gauss’s Law
A uniform E-field ‘E’ points from left to right. This E-field passes through a closed hemispherical
dome as shown below. The dome consists of two parts – a circular base and an open hemisphere
each of radius ‘R’. What is the magnitude of the electric flux through the open hemisphere part
of the closed dome? (hint: the flux through the closed dome is equal to the sum of fluxes through
each part of the dome)
Answer ______________________________
9.
Coulomb’s Law
Three equal positive charges are located at three corners of a square of side 2a as shown in the
diagram below. The origin is in the center of the square. What is the x-component of the electric
field at the origin due to this configuration of charges?
Answer ________________________
12
10.
Resistance
Two cylindrical resistors are made from the same material, and they are equal in length. The first
resistor has diameter D, and the second resistor has diameter 2D. If the same current flows
through both resistors, compare the average velocities of the electrons in the two resistors:
L
D
2D
R1
R2
Answer ________________________________
11.
RC Circuits
In the circuit shown below, the switch has been open for a long time.
a ) What is the current through resistor R1 immediately after the switch has been closed?
Answer ___________________
b ) What is the current through resistor R1 long after the switch has been closed?
Answer ___________________
13
12.
Ampere’s Law
Determine the magnitude of the magnetic field B produced above and below a uniform current
density J flowing through a slab of infinite width and thickness d as shown in the diagram below.
Hint: use Ampere's Law.
d
J
J
J
J
J
Answer ________________________
13.
Magnetic Field
A wire of radius 5.0 cm carries a current of 75 A that is uniformly distributed over its cross-sectional
area. What is the magnetic field inside the wire at a distance 3.5 cm from the center?
Answer ________________________
14.
Inductance
A 35.0 mH inductor has a current flowing through it of 52.0 A. How much energy is stored in its
magnetic field?
Answer ________________________
14
15.
Potential
The electric potential in a region of space is given by
ÁÊ
ÁÊ
ÁÊ
V ˜ˆ
V ˜ˆ
V ˜ˆ
V ÊÁË x,y,z ˆ˜¯ = 50 V + ÁÁÁÁ 15 2 ˜˜˜˜ x 2 − ÁÁÁÁ 10 3 ˜˜˜˜ y 3 + ÁÁÁÁ 22 4 ˜˜˜˜ z 4
Ë m ¯
Ë m ¯
Ë m ¯
What is the electric field in this region?
Answer __________________
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Part 3
Comprehensive Problems
Please try to complete as many sections of each problem as you can.
You will receive partial credit for the correct portions of all work that you show.
1. A semi-circular loop of radius ‘a’ carries a total charge ‘+Q’ which is spread uniformly. In this
exercise we will find the total electric field at the center of the half-loop.
a ) From symmetry, what direction do you expect the net E-field to point? ___________
b ) The linear charge density on the ring, λ = _______
c ) Write an expression for the infinitesimal charge element in term of λ.
dq = ________
d ) Write an expression for the E-field from the charge element at the center of the ring.
dE = __________________
e ) Modify dE to represent the E-field component in the direction you found in part (a)
= ____________________
f ) Find the total field at the center by integrating
E = _________________
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over the entire ring.
2. A thin strip of perfectly conducting metal of height h = 33.0 cm moves through a static magnetic
field of strength B = 1.20 T at a velocity v = 133 cm/s as shown in the diagram below.
a) Find the magnetic force felt by a free electron in the metal strip
Answer ____________
b) Find the electric field strength necessary to counteract the magnetic force you found in (a)
Answer ____________
c) Using the result from part (b), calculate the Voltage (potential difference) between the top and
bottom of the strip
Answer ____________
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3. A negative point charge ‘-Q’ is placed at the center of a neutral conducting shell of inner radius
‘a’ and outer radius ‘b’. (DRAW A PICTURE)
a) The induced charge on the inner surface of the conducting shell is ________, and the induced
charge on the outer surface of the conducting shell is _________.
b) Write an expression for the electric field in terms of the variable ‘r’ for the electric field inside
the conducting shell, that is, when r < a. Give at reason for your answer.
E = ______________
c) What is the field within the conducting shell itself ( a < r < b )? Give at reason for your answer.
E = _______________
d) What is the E-field outside the conducting shell? Give a reason for your answer.
E = _______________
e) What is the electric potential at the outer surface of the conducting shell? (show work)
V (b ) = ______________
f) What is the electric potential at the inner surface of the conducting shell? (show work)
V (a ) = ______________
g) What is the electric potential at a distance r =
V (a / 2) = ______________
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a
from the center? (show work)
2
4. A semicircular loop of radius R carries a clockwise current I. This loop is immersed in a uniform
magnetic field B that points vertically upward.
a) What is direction of the net force on the semicircular loop? _________________
Hint: the loop is half of a dipole. Which way does it want to point?
b) What is the angle between the infinitesimal element dL and the magnetic field?
angle = ______________ (in terms of θ)
c) Write an expression for the force on the current element dL. Give the direction too.
dF = _________________
;
Direction = _______________
d) Find the total force on the by integrating over the individual forces on each element.
F = _____________________
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5. Two thin conducting slabs of width w are separated by a distance d. Current I flows uniformly in
both slabs, but in opposite directions with respect to one another. This pair of slabs acts like an
inductor. Assume d <<w (hint: what is this assumption telling you?)
a ) What is the direction of the magnetic field between the slabs? ___________
b ) What is the magnitude of the field between the slabs? Hint: Use Ampere’s Law
B = ______________________
c ) If the slabs have length l, what is the total flux between them?
Φ = ____________________
d ) What is the inductance of this pair of slabs?
L = _____________________
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6. Consider a conducting cylindrical shell of inner radius ‘a’, outer radius ‘b’, height ‘h’ and
resistivity ‘ρ’. This cylindrical shell is used as a resistor such that the current flows uniformly
from the inside surface to the outer surface. Draw a picture!
a) Consider a very thin shell within the cylinder at a radius r and with thickness dr. If you were to
cut this shell lengthwise and lay it out flat, what would be the dimensions of this thin slice of the
shell?
height = _________ ;
thickness = dr
;
width (circumference) = ____________
b) Write an expression for the differential resistance dR of this thin slice of the cylindrical shell.
Remember that the current is flowing straight through the shortest way.
dR = _______________
c) Find the resistance of the entire cylindrical shell by integrating dR over all the slices that the
current must pass through..
R = _______________
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