Download PHYS 6000 C01, Spring 2003

PHYS 208-GH, Fall 2005
Final Exam (Monday, December 19)
1. We use a telescope to observe two distant points sources 2.5m apart with light of 600nm. The slit in the
telescope has a width of 0.35mm. What is the maximum distance in meters at which the two sources maybe
distinguished if the resolution is diffraction limited and Rayleigh’s criterion is used?
2. Let’s consider a long solid cylinder with radius R that has positive charge uniformly distributed
throughout it, with charge per unit volume . a) Find the electric field inside the cylinder at a distance r
from the axis in terms of . b) Find the electric field at a point outside the cylinder in terms of the charge
per unit length . c) Compare the answers to parts (a) and (b) for r = R.
3. In the circuit on the right, the two capacitors are charged by a 12.0 V battery with an internal resistance
of 1.0 . There is a 5.0  resistor in series between the capacitors. a) What is the time constant of the
charging circuit? b) After the switch has been closed for time determined in part (a), what is the voltage
across the 3.0 F capacitor?
4. A circular loop has radius R and carries current I2 in a clockwise direction. The center of the loop is a
distance D above a long, straight wire. What are the magnitude and direction of the current I1 in the wire if
the magnetic filed at the center of the loop is zero?
5. In an L-R-C series circuit, R= 150 , L = 0.750 H, and C = 0.0180 F. The source has voltage amplitude
of 150 V and the frequency of the source is tuned to the resonance frequency the circuit. a) What is the
power factor? b) What is the average power delivered by the source? c) The capacitor is replaced by one
with C = 0.0360 F and the source frequency is adjusted to the new resonance value. Then what is the
average power delivered by the source?
6. Your cell phone emits a sinusoidal electromagnetic wave with a wavelength of 35.4 cm and an electric
field amplitude of 5.4 x 10-2 V/m at a distance of 250 m from the antenna. Calculate a) the frequency of the
wave; b) the magnetic field amplitude; c) the intensity of the wave. (Note that: 0= 4 x 10-7 N/A2)
7. A bar of length L = 0.8 m is free to slide without friction on horizontal rails. There is a uniform magnetic
filed B = 1.5 T directed into the page. A one end of the rails there is a 12.0 V battery and a switch. The bar
has mass 0.9 Kg and resistance 5.0 . The switch is closed at time t = 0. a) Find the acceleration of the bar
as a function of the speed. b) What is the acceleration of the bar when its speed is 2.0 m/s? c) What is the
terminal speed of the bar? d) Find an expression of the speed as a function of time.