Page 1

(Similar to 22-A2 and 22-A8) A deuteron is sailing along one sunny day traveling North through the earth’s magnetic field.

Given: A deuteron has as much charge as an electron but positive. It is traveling at 2 x 10⁷ m/s. The earth's magnetic field at that place is 0.55 x 10^-4 T, and the angle of dip is 70^o. (For Sky’s benefit, the sine of 70 ^o is 0.9397 and the cosine of 70^o is 0.3420.)

 Find: (a) What is the vertical component of the earth’s magnetic field?
[0.5 x 10^-4 T]

(b) What the magnitude of the force acting on the deuteron?
[1.7 x 10^-16 N]

(c) What is the direction of the force acting on the deuteron?
[West (2pts for East)]

Page 2

(Similar to 22-B6) In a classroom demonstration of the magnetic force on a current carrying wire, we passed the current from a lantern battery through a horizontal metal rod hanging from a ring stand frame. A strong magnet was arranged to produce a vertically upward magnetic field over part of the metal rod.

Given: The magnet produced a magnetic field of 0.5 T over 10 cm of the metal rod. Suppose the current in the rod was 20 A from North to South.

Find: (a) What is the direction of the force acting on the rod?
[West if upward (East if downward)]

(b) What is the magnitude of the force acting on the rod?
{1 N]

Page 3

23-B10 (with a part added) To block noise above a certain frequency in a public address audio amplifier, a coil having negligible dc resistance is connected in series with the input resistor of the amplifier’s input stage.

Given: The inductance of the coil is 15 mH. At 8 kHz the reactance of the coil equals the resistance of the input resistor.

Find: (a) What is the reactance of the coil at that frequency?
[ 750 Ω ]

(b) What is the impedance of the coil and resistor combination?
[  1.1 k Ω ]

Page 4

 23-C3 referring to B3 (sister using same numbers)   An electric drill runs at full speed when it turns fast enough that, ignoring mechanical friction and electrical resistance, the back emf equals the forward emf. Under load, the motor runs slower and the back emf drops. The motor then draws more power. A simplified model of a shunt wound motor in which the field and armature windings are connected in parallel is to think of the current through the stationary field winding as being constant while the current through the rotating armature as being proportional to speed.

Given:  A Model R7100 Heavy Duty ½ inch drill, made by Ridgid® will turn at 3,000 rpm under no load. Cutting a ¾ inch hole through wood, however, it turns at 2,000 rpm. Running on 120 V direct current, the drill draws 6 A under load but only 2 A with no load. The resistance of the armature is  2 Ω and the line voltage is 120 V. (Too much information. Two answers possible.

Find: (a) How much current flows through the armature under load?
[ 2 A]

(b) How much current flows through the field coil?
[ 0 A }

(c) How much is the resistance of the field coil?
[ 60 Ω }

(d) What is the back voltage in the armature under load?
[ 80 V }

Page 5

Image of Sputnik (above) and split dipole antenna (below) with gray area indicating a reflection in the body of the satellite.

24-A2 (Sister)According to NASA, “History changed on October 4, 1957, when the Soviet Union successfully launched Sputnik I. The world's first artificial satellite was about the size of a basketball, weighed only 183 pounds, and took about 98 minutes to orbit the Earth on its elliptical path.” Sputnik I emitted a radio signal AM modulated to form beeps that people could pick up on short-wave radio.

Given: Sputnik sent telemetry at 20 and 40 MHz using split dipole antennas (as discussed in class when we spoke of broadcast radio antennas).

Find: (a) What was the shortest wavelength of the telemetry beeps that were emitted by Sputnik?
[ 7.5 m]

(b) What was the length of the antennas that needed to be mounted on Sputnik?
[ 3.25 m ]

Page 6

An old fashioned home-brew crystal radio receivers built by a grade school friend of mine used a coil wound on an oatmeal tube. A more modern version I found on the web uses a coil wound on a discarded cardboard tube from a toilet paper roll. Either way, it is connected in parallel with a capacitor, shown at left as C1, to tune the receiver. The AM Medium wave  frequency band is 520–1,710 kHz. (The circuit at left is a slightly simplified form of what is available from http://www.hobbytron.com/8893.html. for about  $13.00 The other capacitor, by the way, is used to resonate with the earphone at audio frequencies.)

Given:  Suppose the coil has an inductance of 230 µH coil. The oldest surviving Arkansas radio station, which is KUOA, broadcasts at a frequency of 1290 kHz

Find: (a) What is the value of the capacitor?
[ 66 pF ]

(b) What is the wavelength of KUOA?
[ 233 m]