PHYS 202 Test #2 2/27/09 Dr. Holmes NAME
DO ALL EIGHT PROBLEMS. THE WORTH OF EACH PROBLEM IS MARKED NEXT TO THE PROBLEM. SHOW YOUR WORK FOR PARTIAL CREDIT.
(Use the six directions: N, ® E, ¯ S, ¬ W, ¤ up or out, and Ä down or in.)
1) Consider a proton moving ¬ W at a speed of 2 x 104 m/s in a magnetic field of strength 0.024 T directed Ä down.
a) What is the magnitude of the magnetic force on the proton?
7.68 x 10-17 Nt.
b) What is the direction of the magnetic force on the proton?
¯
S.
c) What is the magnitude of the acceleration on the proton due to this force?
4.60 x 1010 m/s2 .
d) Will this force cause the proton to speed up, slow down, or change direction?
Change direction.
e) Would the magnetic force on an alpha particle (2 protons and 2 neutrons stuck together) moving at the same speed in the same direction through the same field be greater, the same, or less in magnitude than on the proton?
Greater.
f) Would the magnetic force on the alpha at the same speed in the same direction through the same field be in the same, opposite, or other direction than on the electron?
Same.
g) Would the acceleration of the alpha be the same, bigger or smaller than the acceleration of the proton?
Smaller.
2) A certain mass spectrograph consists of a magnet of strength 800 Gauss and the singly charged ions are injected into the field with a speed of 1.64 x 10+4 m/s.
a) If the ions move along a circular path of radius 9.0 cm, what is the mass of these ions (in kg)?
7.02 x 10-26 kg.
b) What is the mass of these ions in amu (atomic mass units)?
42 amu
c) Will oxygen atoms with an atomic mass of 16 amu have a bigger, the same or smaller orbit than those of part a (assuming they have the same speed in the same field)?
Smaller.
d) If a stronger magnet is used in the instrument, will the radius of the ion’s circular path be smaller, the same, or larger?
Smaller.
3) a) How much current would have to flow through a coil of wire to generate a magnetic field of strength 215 Gauss at the center of the coil if the coil had a radius of 9 cm and has 750 turns?
4.11 A .
b) If the radius of the coil were decreased by a factor of 1/3 (to 3 cm) and the number of turns was increased by a factor of 3 (to 2,250) so the amount of wire used was kept the same, what would the field strength at the center become?
1,935 Gauss (9 tmes bigger).
4) a) DESIGN an electric motor that gives an average torque of 0.42 Nt-m. To do this, draw a picture and then specify the values of all the relevant parameters:
b) If this rotates at 60 cycles per second, what is the average power of this motor?
in
5) DESIGN an electric generator that will provide 110 volts rms at 60 cycles/second:
To do this, draw a picture and then specify the values of all the relevant parameters:
6) (a) If the rms-voltage of a household electrical receptacle is 110 volts at 60 Hz, what is the peak voltage at the outlet?
156 Volts.
b) What is the rms-current in a 100 Watt light bulb that is connected across the 110 volt-rms outlet?
0.91 Amps.
c) At 8 cents per kilowatt-hr, how much will it cost to keep the lightbulb on for one month (30 days) ?
$5.76/month .
Assume that a 40 Watt light bulb replaces the 100 Watt light bulb.
d) With this new lower-wattage bulb, will the rms-current be bigger, remain the same, or smaller?
Smaller.
7) In each of the four diagrams below, indicate on the A circuit the direction of the induced current in circuit A due to the situation described (if no current, then write the word NONE on circuit A):
a) the
external magnetic field directed UP through circuit A is DECREASING in
strength:
b) the
South pole of the bar magnet is moved away from the solenoid (cylinder wrapped
with wire) in circuit A:
"
c) the
bar is moving to the right:
d) the
switch in circuit B is being CLOSED (it was open):
8) Consider a series RLC circuit with an oscillating voltage source of 30 volts (rms) at 630 Hz.
The resistance is 10 W , the capacitance is 22 m F, and the inductance is 3 mH.
a) What is the capacitive reactance (XC) ?
11.48 W
b) What is the inductive reactance (XL) ?
11.88 W
c) What is the impedance (Z) of the circuit?
10.01 W
d) What is the rms current through this circuit?
3.0 Amps.