Download Physics 203 Sample Exam 1

Physics 223 Sample Exam 1
Gothard Grey
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Spring 2008
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Name _________________
Mass of proton = 1.67E-27 kg
Mass of alpha = 4 x mass of proton
Charge of alpha = +4e
Fe  ke
[10] = = = =
dE 

q1q2
 q2 E
r2
Fm  qv  B  I  B
1
dq
rˆ
4 o r 2
E dA 
Surface
1
o
dB  o

 dq
Id  rˆ
r2
B d  o I
Curve
Electromagnetic Units
in terms of:
Unit
V
J/C = V
C
T
H
J
N
t
fundamental
J/C
T·m^2/s
H·A/s
J/C
N·m/C
J/A·s
kg·m^2/A·s^3
N·s/m·T
J·s/A·H
J/V
N·m/V
A·s
A·s
N/m·T
V·s/H
J/V·s
N·m/V·s
C/s
A
s/F
kg·m^2/A^2·s^3
A·s = C
J/V
A
V/Ω
C/s
V/A =Ω
V/A
V·s/C
F = C/V
C/V
C/V
T V·s/m^2
H
Wb=T·m^2
H·s
kg/T^2·m^2
kg/C·s
V·s/A
T·s·m^2/C
T·m^2/A
V·s
H·C/s
T·m^2
J·s/C^2 N·s·m/C^2
1/H
C^2/J
C^2/N·m
s/Ω
A^2•s^4/kg·m^2
H·A/m^2
J/m^3
N·s/C·m
kg/C·s
kg/A·s^2
J/C^2
N·m/C^2
Ω·s
kg·m^2/A^2·s^2
J/A
N·m/A
V·s
kg·m^2/A·s^2
H·A
Multiple choice, 3 points each
[1] An electron, a proton and an alpha particle enter a uniform magnetic field, all moving
at the same velocity. The particle with the largest radius for its trajectory is the
(a) electron.
(b) proton.
(c) alpha particle.
(d) all the same.
[2] For the particles in question 1, which particle curves in the opposite direction from
the other two upon entering the field?
(a) electron.
(b) proton.
(c) alpha particle.
(d) all the same.
[3] As you move away from a long, straight wire carrying an electric current, the strength
of the magnetic field varies as
(a) 1/r2
(b) 1/r
(c) ln(r)
(d) r
[4] A magnetic field exerts a force on all the following EXCEPT
(a) a current carrying wire (b) a moving electric charge
(c) a stationary electric charge
(d) a magnet
[5] Which of the following will not drive an electric current in a conductive loop?
(a) magnetic flux through the loop
(b) a potential difference along the loop
(c) an electric field around the loop (d) a changing magnetic flux through the loop
[6] The presence of a ferromagnetic core in the center of a coil, in part,
(a) concentrates the magnetic field. (b) spreads the magnetic field lines out.
(c) only serves to support the coil. (d) is necessary to produce a magnetic field.
[7] A light wave is made of
(a) constant electric and magnetic fields.
(b) oscillating electric and magnetic fields in the same direction.
(c) electric and magnetic fields at various angles.
(d) oscillating electric and magnetic fields at right angles.
[8] Magnetic fields can be produced by
(a) electric currents
(b) changing electric flux
(c) both a and b
(d) none of these
[9] Two wires, each carrying a current of 200 mA cross over one another at a 90° angle.
The magnetic force between them
(a) is attractive. (b) is zero.
(c) is repulsive.
(d) depends on the direction of the currents.
[10] The energy stored in a magnetic field is proportional to
(a) 1/B2
(b)1/B
(c) B
(d)B2
Choose one of problems A or B to do. Show all work. If you have extra time, you
may work on the other for extra credit. 5 points per part.
[A] Two solenoids are next to each other, oriented end to end along the same axis.
Solenoid A is 20 cm long, 4 cm. in diameter and has 200 turns.
Solenoid B has 5 turns per cm., is 15 cm long and 5 cm. in diameter.
(a) Calculate the inductance of solenoid B.
(b) Given a current of 4sin(10t) in solenoid A, calculate the flux in solenoid B. You may
assume no leakage of field from between the solenoids .
(c) Calculate the induced voltage in solenoid B given a magnetic field of 4sin(20t)
everywhere inside it.
(d) For a current of 2 Amps in solenoid A, calculate the magnetic field inside solenoid A.
(e) A proton from a cosmic ray enters the field on a path perpendicular to the axis of the
solenoid. Calculate the radius of the path of the proton in the field.
[B] Electrons are held in a circular path of 2 km. radius and are moving at a velocity of
3.0E6 m/s. A total of 10E10 electrons are in the beam.
(a) This beam has what current?
(b) What magnetic field does this beam produce at the center of the 2km ring?
(c) What is the cyclotron frequency for the electrons in this beam?
(d) To keep the electron beam in its circular path, what magnetic field must be used and
what direction does it point if the beam circulates clockwise?
(e) If a magnetic field of 0.2 Tesla is produced with a solenoid carrying a current of 5
Amps, what can you say about the construction of the solenoid (number of coils, length,
area,..)?
Do one of questions C and D, 20 points.
[C] A square loop, a cm x b cm, lies on a table with 2 wires. One wire carries 2 amps, is
parallel to the side of length b and is y cm away from the closest side. The second wire
carries 5 amps, is parallel to the side of length a and is x cm away.
(a) Draw a diagram.
(b) Derive the expression for the magnetic field produced by each current.
(c) Derive the total magnetic flux in the loop using superposition.
[D] A long solenoid with n turns per meter carries current I in the wire. The solenoid has
radius R.
(a) Use Ampere’s Law to find the magnetic field inside the solenoid.
(b) Determine the magnetic flux inside the solenoid.
(c) A particle with mass m and charge q enters the field along a path making an angle of
45 with the axis of the solenoid. Find an expression for its trajectory. You can split the
trajectory into two motions to make it simpler.