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Physics 210 Final Exam 2008
PHYSICS 210 FINAL EXAM
CAMOSUN COLLEGE
DEC. 2008
Instructor: Julie Alexander
Total marks = 90 Name ______
Please show all or your work in the space provided. Part marks will be awarded for work shown. Calculators are allowed. A formula sheet is provided.
1) A ring of radius R carries a uniformly distributed positive total charge Q. Calculate the magnitude and direction of the electric field due to the ring at a point P lying a distance x from its center along the central axis perpendicular to the plane of the ring. (8 marks).
R
x
P
2) An infinitely long cylindrical insulating shell of inner radius a and outer radius b has a uniform volume charge density ρ. A line of uniform linear charge density λ is placed along the axis of the shell.
a) Determine the electric field for r<a. (3 marks)
b) Determine the electric field for a<r<b. (4 marks)
c) Determine the electric field for rb. (3 marks)
3) A particle (charge = +1.5 mC) moving in a region where only electric forces act on it has a kinetic energy of 5.0 J at point A. The particle subsequently passes through point B which has an electric potential of +1.7 kV relative to point A. Determine the kinetic energy of the particle as it moves through point B. (4 marks)
a. / 3.5 Jb. / 2.5 J
c. / -2.5 J
d. / 7.5 J
e. / -5.5 J
4)A charge per unit length given by λ(x) = bx, where b = 14 nC/m2, is distributed along the x axis from x = +10 cm to x = +16 cm. If the electric potential at infinity is taken to be zero, what is the electric potential at the point P on the y axis at y = 12 cm? (4 marks)
a. / 524 Vb. / 7.2 V
c. / 9.0 V
d. / 5.5 V
e. / 8.1 V
5)A small bulb is rated at 9.0 W when operated at 125 V. The tungsten filament has a temperature coefficient of resistivity α = 4.5 X 10-3 / oC. When the filament is hot and glowing, its temperature is seven times room temperature (20 oC). What is the resistance of the filament (in ohms) at room temperature? (4 marks)
a. / 1127.b. / 1275.
c. / 2080.
d. / 4560.
e. / 5590.
6)In the figure, if a = 3.0 cm, b = 5.0 cm, and I = 4.0 A, what is the magnitude of the magnetic field at point P? (4 marks)
a. / 49 μT
b. / 32 μT
c. / 44 μT
d. / 59 μT
e. 18 μT
7) A parallel-plate capacitor in air has a plate separation of 1.50 cm and a plate area of 25.0 cm2. The plates are charged to a potential difference of 250 V and disconnected from the source. The capacitor is then immersed in distilled water that has a dielectric constant of 80.0. Assume the liquid is an insulator.
a) Determine the capacitance before and after immersion.(3 marks)
b) Determine the charge on the plates before and after immersion.(2 marks)
c) Determine the potential difference between the plates after immersion.(2 marks)
d) Determine the change in energy of the capacitor.(3 marks)
8) At TRIUMF protons (m=1.67X10-27 kg, q=1.6X10-19C) are accelerated through a potential difference of 300kV before entering the cyclotron where the magnetic field has a strength of 0.3 T. (1eV=1.6X10-19J)
a) Calculate the radius of the proton’s first turn.(4 marks)
b) After entering the cyclotron the proton passes through the D gap twice for every full circle of its path. The D gap voltage is 200 kV. Calculate the radius of the proton’s path after it has undergone 1000 full revolutions.(4 marks)
c) What is the cyclotron frequency of the protons?(4 marks)
d) If the protons make a total of 1500 revolutions before leaving the cyclotron how long do they spend it the machine.(3 marks)
9) Shown below is a cross-sectional view of a coaxial cable. The center conductor is surrounded by a rubber layer, which is surrounded by an outer conductor, which is surrounded by another rubber layer. In a particular application, the current in the inner conductor is 1.00 A out of the page and the current in the outer conductor is 3.00 A into the page.
a) Determine the magnitude and direction of the magnetic field at point a, 1mm from the center of the cable. (4 marks)
b) Determine the magnitude and direction of the magnetic field at point b, 3 mm from the center of the cable.(4 marks)
10) Consider the arrangement shown below. Assume that R = 8.00 Ω, ℓ = 3.20 m, and a uniform 2.40-T magnetic field is directed into the page.
a) At what speed should the bar be moved to produce a current of 0.500 A in the resistor?(4 marks)
b) Calculate the applied force required to move the bar to the right at a constant speed of 3.00 m/s (the current will no longer be 0.5A) (4 marks)
c) At what rate is energy delivered to the resistor when the velocity is 3 m/s?
(3 marks)
d) What is the direction of the induced current through the resistor? (2 marks)
11) Clever farmers whose lands are crossed by large power lines have been known to steal power by stringing wire near the power line and making use of the induced current – a practice that has been ruled legally to be theft. The scene of a particular crime is shown below. The power line carries 60 Hz alternating current with a peak current of 10kA (that is, the current is given by I=Iosinωt, where Io=10kA and ω=2πf, with f=60Hz).
a) If the farmer wants a peak voltage of 170 V, what should be the length, L, of the loop? (170V is the peak of standard 120V AC power). (5 marks)
b) If all the equipment the farmer connects to the loop has an equivalent resistance of 5.0 Ω, what is the farmer’s average power consumption? (Note: The average power consumption is half the product of the peak voltage and peak current in the loop.) (3 marks)
c) If the power company charges 6 cents per kWh, what is the monetary value of the energy stolen each day? (2 marks)