12.3 The electric field strength of a velocity selector is 345 N/C. The magnetic field strength is 1.34 T. Charged alpha particles
having a mass of 6.68×10í^27 kg pass through the selector. What is the final kinetic energy of each one?
J12.4 The oppositely charged plates of a velocity selector are separated by 4.5 cm. The uniform magnetic field is supplied by a
current-carrying solenoid that encloses the selector, and it has a strength of 0.35 T. What potential difference needs to be
applied across the charged plates in order to select a particle velocity of 3.2×10^4 m/s?
V12.5 A velocity selector of length 0.25 m has a magnetic field of 5.0×10í^3 T and an electric field of 50 N/C. Electrons are injected
into the apparatus and must pass through a slit at the far end which is exactly 1.0 cm across. (a) What is the velocity of a
particle that goes through the velocity selector undeflected? (b) By how much can the velocity be increased or decreased
from the undeflected value and still make it through the velocity selector? Assume the following: (1) The electrons begin their
journey aligned with the center of the slit. (2) The magnetic force always acts in the same direction (that is, it causes an
acceleration that we can approximate as linear). This is justified so long as the slit width is much smaller than the length of the
velocity selector. (3) The ratio of the ideally selected velocity and the difference between the maximum and minimum
velocities is very small. This will allow you to simplify some of your calculations. The final answer will demonstrate that this
assumption is also justified.
(a) m/s
(b) m/sSection 13 - Circular motion of particles in magnetic fields
13.1 A proton moves perpendicularly to a uniform magnetic field of strength 0.0585 T at a speed of 15,400 m/s. What is the radius
of the circle it describes?
m13.2 A charged particle moves in a concentric circular orbit inside a solenoid made of very thin wires, with a diameter of 10.4 cm,
just missing the inner surface of the solenoid coils. The charge on the particle is 3.00 μC, its speed is 550 m/s, and the
strength of the field inside the solenoid is 0.734 T. What is the mass of the particle?
kg13.3 How fast must an alpha particle (m = 6.68×10í^27 kg, q = 3.20×10í^19 C) travel perpendicularly to the Earth's magnetic field in a
laboratory (B = 5.02×10í^5 T) for it to describe a circular path of radius 2.34 cm?
m/s13.4 A mad scientist has designed a new line of highly stylish, Italian-cut Kevlar body armor suits. In order to test one of these
suits he wishes to shoot himself, using a .22 caliber rifle that fires rounds weighing 3.56×10í^3 kg with a velocity of 762 m/s. To
shoot himself, he will fire the gun into a vertically oriented magnetic field of strength 1.25 T, hoping that the bullet will follow a
semi-circular path, emerge from the field, and fly straight toward him, striking the body armor. In order for the bullet to hit him
he needs to have the bullet circle through a small radius of 2.00 cm. Finally, he knows that in order to be deflected by the
magnetic field, the flying bullet needs to be electrically charged, so the firearm has an insulating rubber grip and is wired to a
static electricity generator. What magnitude of charge must be placed on the bullet for the scientist's mad scheme to
succeed? (The answer will be impractically large, because the scientist is truly mad.)
C13.5 What is the period of the orbit for a particle of mass 7.00×10í^6 kg and charge 2.00×10í^6 C circulating in a 6.00eí2 T
magnetic field?
s13.6 A particle with mass 1.65×10í^12 kg and electric charge í8.22×10í^8 C moves perpendicularly to a uniform magnetic field of
strength 5.45×10í^3 T. The angular momentum of the particle about the center of its circular orbit is 3.20×10í^10 kg·m^2 /s. (a)
What is the radius of the circular orbit? (b) What is the speed of the particle?
(a) m
(b) m/s13.7 An ionized hydrogen atom (that is, a free proton) is moving through the magnetic field of the Milky Way galaxy, at a location
distant from any star. The kinetic energy of the proton is 5.60 keV, and it moves through a circular path having a radius of
0.0317 astronomical units. An astronomical unit (AU) equals the average radius of the Earth's orbit around the Sun,
1.50×10^11 m. What is the strength of the galactic magnetic field in this region of space?
T13.8 A sodium ion with mass 2.32×10í^26 kg and charge +1.60×10í^19 C is moving with velocity 3.00×10^5 m/s in the positive x
direction. An identical particle is moving with the same speed in the negative x direction, but displaced by +1.50 m in the y
direction. When the x coordinates of the atoms are equal, a magnetic field perpendicular to their motion is turned on so that